দেওয়া আছে,
$x=\frac{\sqrt{2a+3b}+\sqrt{2a-3b}}{\sqrt{2a+3b}-\sqrt{2a-3b}}$
বা, $\frac{x+1}{x-1}=$$\frac{\left(\sqrt{2a+3b}+\sqrt{2a-3b}\right)+\left(\sqrt{2a+3b}-\sqrt{2a-3b}\right)}{\left(\sqrt{2a+3b}+\sqrt{2a-3b}\right)-\left(\sqrt{2a+3b}-\sqrt{2a-3b}\right)}$
[যোজন-বিয়োজন করে]
বা, $\frac{x+1}{x-1}=$$\frac{\sqrt{2a+3b}+\sqrt{2a-3b}+\sqrt{2a+3b}-\sqrt{2a-3b}}{\sqrt{2a+3b}+\sqrt{2a-3b}-\sqrt{2a+3b}+\sqrt{2a-3b}}$
বা, $\frac{x+1}{x-1}=$$\frac{2\sqrt{2a+3b}}{2\sqrt{2a-3b}}$
বা, $\frac{x+1}{x-1}=$$\frac{\sqrt{2a+3b}}{\sqrt{2a-3b}}$
বা, $\left(\frac{x+1}{x-1}\right)^2=$$\left(\frac{\sqrt{2a+3b}}{\sqrt{2a-3b}}\right)^2$
[উভয় পাশে বর্গ করে]
বা, $\frac{\left(x+1\right)^2}{\left(x-1\right)^2}=$$\frac{2a+3b}{2a-3b}$
বা, $\frac{x^2+2x+1}{x^2-2x+1}=$$\frac{2a+3b}{2a-3b}$
বা, $\frac{\left(x^2+2x+1\right)+\left(x^2-2x+1\right)}{\left(x^2+2x+1\right)-\left(x^2-2x+1\right)}=$$\frac{\left(2a+3b\right)+\left(2a-3b\right)}{\left(2a+3b\right)-\left(2a-3b\right)}$
[পুনরায় যোজন-বিয়োজন করে]
বা, $\frac{x^2+2x+1+x^2-2x+1}{x^2+2x+1-x^2+2x-1}=$$\frac{2a+3b+2a-3b}{2a+3b-2a+3b}$
বা, $\frac{2x^2+2}{4x}=$$\frac{4a}{6b}$
বা, $\frac{2\left(x^2+1\right)}{4x}=$$\frac{4a}{6b}$
বা, $\frac{\left(x^2+1\right)}{2x}=$$\frac{2a}{3b}$
বা, $3b\left(x^2+1\right)=$$2a\cdot2x$
বা, $3bx^2+3b=$$4ax$
$\therefore 3bx^2-4ax+3b=0$ [দেখানো হলো]
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