If a^4 + 1/a^4 = 1154, then the value of a^3 + 1/a^3 is

Question

If \(a^4 + \frac{1}{a^4}\) = 1154, then the value of \(a^3 + \frac{1}{a^3}\) is  

(a) 198 

(b) 216 

(c) 200 

(d) 196

Answer 1

(a) 198

  \(a^4 + \frac{1}{a^4}\) = 1154 ⇒ \(a^4 + 2 + \frac{1}{a^4}\) = 1154 + 2

⇒ \(\bigg(a^2+\frac{1}{a^2}\bigg)^2\) = 1156 ⇒ \(a^2 + \frac{1}{a^2} = 34\)

⇒ \(a^2 + 2 + \frac{1}{a^2}\) = 34 + 2 ⇒ \(\bigg(a+\frac{1}{a}\bigg)^2\) = 36

\(a+\frac{1}{a}\) = 6