যদি $a+\frac{1}{a}=5$ হয়, তাহলে $a^6-110a^3+1$ এর মান কত?

দেওয়া আছে,
$a+\frac{1}{a}=5$

প্রদত্ত রাশি,
$a^6-110a^3+1$

$=a^3 \times \frac{1}{a^3}\left(a^6-110a^3+1\right)$

$=a^3 \times \left(\underline{\frac{a^6}{a^3}}-\frac{110a^3}{a^3}+\underline{\frac{1}{a^3}}\right)$

$=a^3 \times \left(\underline{a^3+\frac{1}{a^3}}-110\right)$

$=a^3 \times \left\{\underline{\left(a+\frac{1}{a}\right)^3-3 \cdot a \cdot \frac{1}{a}\left(a+\frac{1}{a}\right)}-110\right\}$

$=a^3 \times \left\{\left(a+\frac{1}{a}\right)^3-3 \cdot \left(a+\frac{1}{a}\right)-110\right\}$

$=a^3 \times \left\{\left(5\right)^3-3 \times 5-110\right\}$

$=a^3 \times \left(125-15-110\right)$

$=a^3 \times \left(125-125\right)$

$=a^3 \times 0$

$=0$

$\therefore$ নির্ণেয় মান $0$