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<title>QnA fy - Recent questions tagged অনুপাত ও সমানুপাত</title>
<link>https://qnafy.com/tag/%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4%20%E0%A6%93%20%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4</link>
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<title>$l,m,n$  ক্রমিক সমানুপাতিক হলে, দেখাও যে, $\frac{l}{n}=\frac{l^2+m^2}{m^2+n^2}$</title>
<link>https://qnafy.com/19376/%24l-m-n%24-%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BF%E0%A6%95-%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4%E0%A6%BF%E0%A6%95-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-l-n-frac-l-2-m-2-m-2-n-2-%24</link>
<category>Math</category>
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<pubDate>Sat, 13 Dec 2025 12:48:30 +0000</pubDate>
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<title>$x:y=7:5$, $y:z=5:7$ হলে $x:z=$ কত?</title>
<link>https://qnafy.com/19346/%24x-y-7-5%24-%24y-z-5-7%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%24x-z-%24-%E0%A6%95%E0%A6%A4</link>
<category>Algebra</category>
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<pubDate>Fri, 10 Oct 2025 10:31:49 +0000</pubDate>
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<title>একটি বর্গের বাহুর দৈর্ঘ্য দ্বিগুণ হলে তার ক্ষেত্রফল কতগুণ বৃদ্ধি পাবে?</title>
<link>https://qnafy.com/19344/%E0%A6%8F%E0%A6%95%E0%A6%9F%E0%A6%BF-%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%97%E0%A7%87%E0%A6%B0-%E0%A6%AC%E0%A6%BE%E0%A6%B9%E0%A7%81%E0%A6%B0-%E0%A6%A6%E0%A7%88%E0%A6%B0%E0%A7%8D%E0%A6%98%E0%A7%8D%E0%A6%AF-%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%97%E0%A7%81%E0%A6%A3-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A4%E0%A6%BE%E0%A6%B0-%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%87%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%AB%E0%A6%B2-%E0%A6%95%E0%A6%A4%E0%A6%97%E0%A7%81%E0%A6%A3-%E0%A6%AC%E0%A7%83%E0%A6%A6%E0%A7%8D%E0%A6%A7%E0%A6%BF-%E0%A6%AA%E0%A6%BE%E0%A6%AC%E0%A7%87</link>
<category>Algebra</category>
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<pubDate>Fri, 10 Oct 2025 10:20:52 +0000</pubDate>
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<title>আরিফ ও আকিবের বয়সের অনুপাত $5:3$, আরিফের বয়স $20$ বছর হলে, কত বছর পরে তাদের বয়সের অনুপাত $7:5$ হবে?</title>
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<category>Algebra</category>
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<pubDate>Fri, 10 Oct 2025 10:02:01 +0000</pubDate>
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<title>$\frac{a}{x}=\frac{m^2+n^2}{2mn}$ হলে $\frac{\sqrt{a+x}}{\sqrt{a-x}}$ কত?</title>
<link>https://qnafy.com/19340/%24-frac-a-x-frac-m-2-n-2-2mn-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%24-frac-sqrt-a-x-sqrt-a-x-%24-%E0%A6%95%E0%A6%A4</link>
<category>Algebra</category>
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<pubDate>Fri, 10 Oct 2025 07:34:54 +0000</pubDate>
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<title>$1011$ টাকাকে $\frac{3}{4}:\frac{4}{5}:\frac{6}{7}$ অনুপাতে বিভক্ত কর।</title>
<link>https://qnafy.com/19332/%241011%24-%E0%A6%9F%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%95%E0%A7%87-%24-frac-3-4-frac-4-5-frac-6-7-%24-%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4%E0%A7%87-%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%95%E0%A7%8D%E0%A6%A4-%E0%A6%95%E0%A6%B0%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Thu, 02 Oct 2025 05:40:10 +0000</pubDate>
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<title>একটি সমিতির নেতা নির্বাচনে দুইজন প্রতিদ্বন্দীর মধ্যে ডোনাল্ড সাহেব $4:3$ ভোটে জয়লাভ করলেন। যদি মোট সদস্য সংখ্যা $581$ হয় এবং $91$ জন সদস্য ভোট না দিয়ে থাকেন, তবে ডোনাল্ড সাহেবের প্রতিদ্বন্দী কত ভোটের ব্যবধানে পরিজিত হয়েছেন?</title>
<link>https://qnafy.com/19327/%E0%A6%8F%E0%A6%95%E0%A6%9F%E0%A6%BF-%E0%A6%B8%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%B0-%E0%A6%A8%E0%A7%87%E0%A6%A4%E0%A6%BE-%E0%A6%A8%E0%A6%BF%E0%A6%B0%E0%A7%8D%E0%A6%AC%E0%A6%BE%E0%A6%9A%E0%A6%A8%E0%A7%87-%E0%A6%A6%E0%A7%81%E0%A6%87%E0%A6%9C%E0%A6%A8-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%80%E0%A6%B0-%E0%A6%AE%E0%A6%A7%E0%A7%8D%E0%A6%AF%E0%A7%87-%E0%A6%A1%E0%A7%8B%E0%A6%A8%E0%A6%BE%E0%A6%B2%E0%A7%8D%E0%A6%A1-%E0%A6%B8%E0%A6%BE%E0%A6%B9%E0%A7%87%E0%A6%AC-%244-3%24-%E0%A6%AD%E0%A7%8B%E0%A6%9F%E0%A7%87-%E0%A6%9C%E0%A7%9F%E0%A6%B2%E0%A6%BE%E0%A6%AD-%E0%A6%95%E0%A6%B0%E0%A6%B2%E0%A7%87%E0%A6%A8%E0%A5%A4-%E0%A6%AF%E0%A6%A6%E0%A6%BF-%E0%A6%AE%E0%A7%8B%E0%A6%9F-%E0%A6%B8%E0%A6%A6%E0%A6%B8%E0%A7%8D%E0%A6%AF-%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE-%24581%24-%E0%A6%B9%E0%A7%9F-%E0%A6%8F%E0%A6%AC%E0%A6%82-%2491%24-%E0%A6%9C%E0%A6%A8-%E0%A6%B8%E0%A6%A6%E0%A6%B8%E0%A7%8D%E0%A6%AF-%E0%A6%AD%E0%A7%8B%E0%A6%9F-%E0%A6%A8%E0%A6%BE-%E0%A6%A6%E0%A6%BF%E0%A7%9F%E0%A7%87-%E0%A6%A5%E0%A6%BE%E0%A6%95%E0%A7%87%E0%A6%A8-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%A1%E0%A7%8B%E0%A6%A8%E0%A6%BE%E0%A6%B2%E0%A7%8D%E0%A6%A1-%E0%A6%B8%E0%A6%BE%E0%A6%B9%E0%A7%87%E0%A6%AC%E0%A7%87%E0%A6%B0-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%80-%E0%A6%95%E0%A6%A4-%E0%A6%AD%E0%A7%8B%E0%A6%9F%E0%A7%87%E0%A6%B0-%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%AC%E0%A6%A7%E0%A6%BE%E0%A6%A8%E0%A7%87-%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%9C%E0%A6%BF%E0%A6%A4-%E0%A6%B9%E0%A7%9F%E0%A7%87%E0%A6%9B%E0%A7%87%E0%A6%A8</link>
<category>Algebra</category>
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<pubDate>Thu, 02 Oct 2025 05:04:52 +0000</pubDate>
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<title>একটি ত্রিভুজের পরিসীমা $36$ সে.মি. এবং বাহুগুলোর দৈর্ঘ্যের অনুপাত $3:4:5$ হলে, ত্রিভুজটির বৃহত্তম বাহুর দৈর্ঘ্য কত সে.মি.? ও ত্রিভুজটির ক্ষেত্রফল কত বর্গ সে.মি.?</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:40:30 +0000</pubDate>
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<title>$1$ ঘন সে.মি. কাঠের ওজন $7$ ডেসিগ্রাম। কাঠের ওজন সমআয়তন পানির ওজনের শতকরা কত ভাগ?</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:39:19 +0000</pubDate>
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<item>
<title>ক, খ, গ, ঘ এর মধ্যে $300$ টাকা এমনভাবে ভাগ করে দাও যেন, ক এর অংশ : খ এর অংশ = $2:3$, খ এর অংশ : গ এর অংশ = $1:2$ এবং গ এর অংশ : ঘ এর অংশ = $3:2$ হয়।</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:39:04 +0000</pubDate>
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<title>তিনজন জেলে $690$ টি মাছ ধরেছে। তাদের অংশের অনুপাত $\frac23$, $\frac45$ এবং $\frac56$ হলে, প্রত্যেক বাহুর পরিমাণ নির্ণয় কর।</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:38:49 +0000</pubDate>
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<title>একটি ত্রিভুজের পরিসীমা $45$ সে.মি.। বাহুগুলোর দৈর্ঘ্যের অনুপাত $3:5:7$ হলে, প্রত্যেক বহুর পরিমাণ নির্ণয় কর।</title>
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<title>ক্রিকেট খেলায় সাকিব, মুশফিকুর ও মাশরাফী $171$ রান করলো। সাকিব ও মুশফিকুরের এবং মুশফিকুর ও মাশরাফীর রানের অনুপাত $3:2$ হলে কে কত রান করেছে?</title>
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<pubDate>Fri, 26 Sep 2025 15:37:51 +0000</pubDate>
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<title>একটি অফিসে $2$ জন কর্মকর্তা, $7$ জন অফিস সহকারী এবং $3$ জন অফিস সহায়ক আছে। একজন অফিস সহায়ক $1$ টাকা পেলে একজন অফিস সহকারী পায় $2$ টাকা, একজন কর্মকর্তা পায় $4$ টাকা। তাদের সকলের মোট বেতন $150,000$ টাকা হলে, কে কত বেতন পায়?</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:37:35 +0000</pubDate>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:37:05 +0000</pubDate>
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<title>একটি আয়তক্ষেত্রের দৈর্ঘ্য $10\%$ বৃদ্ধি এবং প্রস্থ $10\%$ হ্রাস পেলে আয়তক্ষেত্রের ক্ষেত্রফল শতকরা কত বৃদ্ধি বা হ্রাস পাবে?</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:36:48 +0000</pubDate>
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<title>একটি মাঠের জমিতে সেচের সুযোগ আসার আগের ও পরের ফলনের অনুপাত $4:7$। ঐ মাঠে যে জমিতে আগে $304$ কুইন্টাল ধান ফলতো, সেচ পাওয়ার পরে তার ফলন কত হবে?</title>
<link>https://qnafy.com/19307/%E0%A6%8F%E0%A6%95%E0%A6%9F%E0%A6%BF-%E0%A6%AE%E0%A6%BE%E0%A6%A0%E0%A7%87%E0%A6%B0-%E0%A6%9C%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A7%87-%E0%A6%B8%E0%A7%87%E0%A6%9A%E0%A7%87%E0%A6%B0-%E0%A6%B8%E0%A7%81%E0%A6%AF%E0%A7%8B%E0%A6%97-%E0%A6%86%E0%A6%B8%E0%A6%BE%E0%A6%B0-%E0%A6%86%E0%A6%97%E0%A7%87%E0%A6%B0-%E0%A6%93-%E0%A6%AA%E0%A6%B0%E0%A7%87%E0%A6%B0-%E0%A6%AB%E0%A6%B2%E0%A6%A8%E0%A7%87%E0%A6%B0-%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4-%244-7%24%E0%A5%A4-%E0%A6%90-%E0%A6%AE%E0%A6%BE%E0%A6%A0%E0%A7%87-%E0%A6%AF%E0%A7%87-%E0%A6%9C%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A7%87-%E0%A6%86%E0%A6%97%E0%A7%87-%24304%24-%E0%A6%95%E0%A7%81%E0%A6%87%E0%A6%A8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%B2-%E0%A6%A7%E0%A6%BE%E0%A6%A8-%E0%A6%AB%E0%A6%B2%E0%A6%A4%E0%A7%8B-%E0%A6%B8%E0%A7%87%E0%A6%9A-%E0%A6%AA%E0%A6%BE%E0%A6%93%E0%A7%9F%E0%A6%BE%E0%A6%B0-%E0%A6%AA%E0%A6%B0%E0%A7%87-%E0%A6%A4%E0%A6%BE%E0%A6%B0-%E0%A6%AB%E0%A6%B2%E0%A6%A8-%E0%A6%95%E0%A6%A4-%E0%A6%B9%E0%A6%AC%E0%A7%87</link>
<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:36:33 +0000</pubDate>
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<item>
<title>ধান ও ধান থেকে উৎপন্ন চালের অনুপাত $3:2$ এবং গম ও গম থেকে উৎপন্ন সুজির অনুপাত $4:3$ হলে, সমান পরিমাণের ধান ও গম থেকে উৎপন্ন চাল ও সুজির অনুপাত বের কর।</title>
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<category>Arithmetic</category>
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<pubDate>Fri, 26 Sep 2025 15:36:12 +0000</pubDate>
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<title>একটি জমির ক্ষেত্রফল $432$ বর্গমিটার। ঐ জমির দৈর্ঘ্য ও প্রস্থের সঙ্গে অপর একটি জমির দৈর্ঘ্য ও প্রস্থের অনুপাত যথাক্রমে $3:4$ এবং $2:5$ হলে, অপর জমির ক্ষেত্রফল কত?</title>
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<title>জমি ও সিমি একই ব্যাংক থেকে একই দিনে $10\%$ সরল মুনাফায় আলাদা আলাদা পরিমাণ অর্থ ঋণ নেয়। জেমি $2$ বছর পর মুনাফা-আসলে যত টাকা শোধ করে $3$ বছর পর সিমি মুনাফা-আসলে তত টাকা শোধ করে। তাদের ঋণের অনুপাত নির্ণয় কর।</title>
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<pubDate>Fri, 26 Sep 2025 15:34:54 +0000</pubDate>
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<pubDate>Sun, 07 Sep 2025 18:21:49 +0000</pubDate>
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<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:20:01 +0000</pubDate>
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<item>
<title>যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $\frac{a}{c}=\frac{a^2+b^2}{b^2+c^2}$</title>
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<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:19:17 +0000</pubDate>
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<item>
<title>যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $a^2b^2c^2\left(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}\right)$$=a^3+b^3+c^3$</title>
<link>https://qnafy.com/17452/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24a-b-b-c%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24a-2b-2c-2-left-frac-1-a-3-frac-1-b-3-frac-1-c-3-right-%24%24-a-3-b-3-c-3%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:18:50 +0000</pubDate>
</item>
<item>
<title>যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $\frac{abc\left(a+b+c\right)^3}{\left(ab+bc+ca\right)^3}=1$</title>
<link>https://qnafy.com/17451/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24a-b-b-c%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24-frac-abc-left-a-b-c-right-3-left-ab-bc-ca-right-3-1%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:18:24 +0000</pubDate>
</item>
<item>
<title>সমাধান কর: $\frac{1-\sqrt{1-x}}{1+\sqrt{1-x}}=\frac13$</title>
<link>https://qnafy.com/17450/%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A7%E0%A6%BE%E0%A6%A8-%E0%A6%95%E0%A6%B0-%24-frac-1-sqrt-1-x-1-sqrt-1-x-frac13%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:16:41 +0000</pubDate>
</item>
<item>
<title>সমাধান কর: $\frac{a+x-\sqrt{a^2-x^2}}{a+x+\sqrt{a^2-x^2}}=\frac{b}{x}$,$2a&gt;b&gt;0$ এবং $x\neq0$</title>
<link>https://qnafy.com/17449/%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A7%E0%A6%BE%E0%A6%A8-%E0%A6%95%E0%A6%B0-%24-frac-a-x-sqrt-a-2-x-2-a-x-sqrt-a-2-x-2-frac-b-x-%24-%242a-b-0%24-%E0%A6%8F%E0%A6%AC%E0%A6%82-%24x-neq0%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:15:45 +0000</pubDate>
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<item>
<title>সমাধান কর: $81\left(\frac{1-x}{1+x}\right)^3=\frac{1+x}{1-x}$</title>
<link>https://qnafy.com/17448/%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A7%E0%A6%BE%E0%A6%A8-%E0%A6%95%E0%A6%B0-%2481-left-frac-1-x-1-x-right-3-frac-1-x-1-x-%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:15:18 +0000</pubDate>
</item>
<item>
<title>$\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$ হলে, দেখাও যে, $\frac{a^3+b^3}{b^3+c^3}=\frac{b^3+c^3}{c^3+d^3}$</title>
<link>https://qnafy.com/17447/%24-frac-a-b-frac-b-c-frac-c-d-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-a-3-b-3-b-3-c-3-frac-b-3-c-3-c-3-d-3-%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:14:49 +0000</pubDate>
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<item>
<title>$\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$ হলে, দেখাও যে, $\left(a^2+b^2+c^2\right)\left(b^2+c^2+d^2\right)=$$\left(ab+bc+cd\right)^2$</title>
<link>https://qnafy.com/17446/%24-frac-a-b-frac-b-c-frac-c-d-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-left-a-2-b-2-c-2-right-left-b-2-c-2-d-2-right-%24%24-left-ab-bc-cd-right-2%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:14:20 +0000</pubDate>
</item>
<item>
<title>$x=\frac{4ab}{a+b}$ হলে, দেখাও যে, $\frac{x+2a}{x-2a}+\frac{x+2b}{x-2b}=2$, $a\neq b$</title>
<link>https://qnafy.com/17445/%24x-frac-4ab-a-b-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-x-2a-x-2a-frac-x-2b-x-2b-2%24-%24a-neq-b%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:13:26 +0000</pubDate>
</item>
<item>
<title>$x=\frac{\sqrt[3]{m+1}+\sqrt[3]{m-1}}{\sqrt[3]{m+1}-\sqrt[3]{m-1}}$ হলে, প্রমাণ কর যে, $x^3-3mx^2+3x-m=0$</title>
<link>https://qnafy.com/17444/%24x-frac-sqrt-3-m-1-sqrt-3-m-1-sqrt-3-m-1-sqrt-3-m-1-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24x-3-3mx-2-3x-m-0%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:13:10 +0000</pubDate>
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<title>$x=\frac{\sqrt{2a+3b}+\sqrt{2a-3b}}{\sqrt{2a+3b}-\sqrt{2a-3b}}$ হলে, দেখাও যে, $3bx^2-4ax+3b=0$</title>
<link>https://qnafy.com/17443/%24x-frac-sqrt-2a-3b-sqrt-2a-3b-sqrt-2a-3b-sqrt-2a-3b-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%243bx-2-4ax-3b-0%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:12:51 +0000</pubDate>
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<title>$\frac{a^2+b^2}{b^2+c^2}=\frac{\left(a+b\right)^2}{\left(b+c\right)^2}$ হলে, দেখাও যে, $a$, $b$, $c$ ক্রমিক সমানুপাতী।</title>
<link>https://qnafy.com/17442/%24-frac-a-2-b-2-b-2-c-2-frac-left-a-b-right-2-left-b-c-right-2-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24a%24-%24b%24-%24c%24-%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BF%E0%A6%95-%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4%E0%A7%80%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:12:37 +0000</pubDate>
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<item>
<title>$\frac{x}{b+c}=\frac{y}{c+a}=\frac{z}{a+b}$ হলে, প্রমাণ কর যে, $\frac{a}{y+z-x}=\frac{b}{z+x-y}=\frac{c}{x+y-z}$।</title>
<link>https://qnafy.com/17441/%24-frac-x-b-c-frac-y-c-a-frac-z-a-b-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24-frac-a-y-z-x-frac-b-z-x-y-frac-c-x-y-z-%24%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:12:18 +0000</pubDate>
</item>
<item>
<title>$\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}$ হলে, প্রমাণ কর যে, $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$।</title>
<link>https://qnafy.com/17440/%24-frac-bz-cy-a-frac-cx-az-b-frac-ay-bx-c-%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24-frac-x-a-frac-y-b-frac-z-c-%24%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:11:55 +0000</pubDate>
</item>
<item>
<title>$\frac{a+b-c}{a+b}=\frac{b+c-a}{b+c}=\frac{c+a-b}{c+a}$ এবং $a+b+c \neq 0$ হলে, প্রমাণ কর যে, $a=b=c$</title>
<link>https://qnafy.com/17439/%24-frac-a-b-c-a-b-frac-b-c-a-b-c-frac-c-a-b-c-a-%24-%E0%A6%8F%E0%A6%AC%E0%A6%82-%24a-b-c-neq-0%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24a-b-c%24</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:11:37 +0000</pubDate>
</item>
<item>
<title>$\frac{x}{xa+yb+zc}=$$\frac{y}{ya+zb+xc}=$$\frac{z}{za+xb+yc}$ এবং $x+y+z \neq 0$ হলে, দেখাও যে, প্রতিটি অনুপাত $=\frac{1}{a+b+c}$।</title>
<link>https://qnafy.com/17438/%24-frac-x-xa-yb-zc-%24%24-frac-y-ya-zb-xc-%24%24-frac-z-za-xb-yc-%24-%E0%A6%8F%E0%A6%AC%E0%A6%82-%24x-y-z-neq-0%24-%E0%A6%B9%E0%A6%B2%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%9F%E0%A6%BF-%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4-%24-frac-1-a-b-c-%24%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:11:13 +0000</pubDate>
</item>
<item>
<title>যদি $(a+b+c)p=$$(b+c-a)q=$$(c+a-b)r=$$(a+b-c)s$ হয়, তবে প্রমাণ কর যে, $\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=\frac{1}{p}$।</title>
<link>https://qnafy.com/17437/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24-a-b-c-p-%24%24-b-c-a-q-%24%24-c-a-b-r-%24%24-a-b-c-s%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3-%E0%A6%95%E0%A6%B0-%E0%A6%AF%E0%A7%87-%24-frac-1-q-frac-1-r-frac-1-s-frac-1-p-%24%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:10:51 +0000</pubDate>
</item>
<item>
<title>যদি $lx=my=nz$ হয়, তবে দেখাও যে, $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=$$\frac{mn}{l^2}+\frac{nl}{m^2}+\frac{lm}{n^2}$।</title>
<link>https://qnafy.com/17436/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24lx-my-nz%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-x-2-yz-frac-y-2-zx-frac-z-2-xy-%24%24-frac-mn-l-2-frac-nl-m-2-frac-lm-n-2-%24%E0%A5%A4</link>
<category>Algebra</category>
<guid isPermaLink="true">https://qnafy.com/17436/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24lx-my-nz%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-x-2-yz-frac-y-2-zx-frac-z-2-xy-%24%24-frac-mn-l-2-frac-nl-m-2-frac-lm-n-2-%24%E0%A5%A4</guid>
<pubDate>Sun, 07 Sep 2025 18:10:32 +0000</pubDate>
</item>
<item>
<title>যদি $\frac{p}{q}=\frac{a^2}{b^2}$ এবং $\frac{a}{b}=\frac{\sqrt{a+q}}{\sqrt{a-q}}$ হয়, তবে দেখাও যে, $\frac{p+q}{a}=\frac{p-q}{q}$।</title>
<link>https://qnafy.com/17435/%E0%A6%AF%E0%A6%A6%E0%A6%BF-%24-frac-p-q-frac-a-2-b-2-%24-%E0%A6%8F%E0%A6%AC%E0%A6%82-%24-frac-a-b-frac-sqrt-a-q-sqrt-a-q-%24-%E0%A6%B9%E0%A7%9F-%E0%A6%A4%E0%A6%AC%E0%A7%87-%E0%A6%A6%E0%A7%87%E0%A6%96%E0%A6%BE%E0%A6%93-%E0%A6%AF%E0%A7%87-%24-frac-p-q-a-frac-p-q-q-%24%E0%A5%A4</link>
<category>Algebra</category>
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<pubDate>Sun, 07 Sep 2025 18:09:47 +0000</pubDate>
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