Question

If $a^4+\frac{1}{a^4}=119$ then find the value of $a^3-\frac{1}{a^3}$

• A. 11
• B. 36
• C. 33
• D. 12

Answer 1

Answer: (B)

36

Given $a^4+\frac{1}{a^4}=119$,
Adding 2 to both sides,
$\therefore a^4+\frac{1}{a^4}+2=121$
$(a^2+\frac{1}{a^2}{)}^2=121$
i.e. $a^2+\frac{1}{a^2}=11$
Subtracting 2 to from sides,
Now, $a^2-2+\frac{1}{a^2}=9$
$(a-\frac{1}{a}{)}^2=9$
i.e. $a-\frac{1}{a}=3$
Now, $a^3-\frac{1}{a^3}=(a-\frac{1}{a})\times (a^2+1+\frac{1}{a^2})=3\times 12=36$