If a^2 + 1/a^2 = 10, then the value of a^4 + 1/a^4 is

Question

If \(a^2+\frac{1}{a^2} = 10,\) then the value of \(a^4+\frac{1}{a^4} \) is

(a) 90 

(b) 98 

(c) 100 

(d) 102

Answer 1

(b) 98

\(a^2+\frac{1}{a^2} = 10\) ⇒ \(\bigg(a^2+\frac{1}{a^2}\bigg)^2 = 10^2\)

⇒ \(a^4+2+\frac{1}{a^4} = 100\) ⇒ \(a^4+\frac{1}{a^4} = 98.\)