SarkariPYQ

SSC CGL 2023 PYQ — Question 74

SSC CGL - 26 July 2023 - Shift 3 • Quantitative Aptitude • Q74

Back to paper

If (x−1x)=10\left(x - \frac{1}{x}\right)=10, what is the value of (x4+1x4)\left(x^4 + \frac{1}{x^4}\right) ?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 10402.

Given that

(x−1x)=10\left(x - \frac{1}{x}\right)=10

Squaring both sides we get

(x−1x)2=102\left(x - \frac{1}{x}\right)^2=10^2

⇒ (x2+1x2−2)=100(x ^2+ \frac{1}{x^2} -2) = 100

⇒ (x2+1x2)=102(x ^2+ \frac{1}{x^2}) = 102

Again squaring both sides we get

(x4+1x4+2)=10404(x ^4+ \frac{1}{x^4} +2) = 10404

⇒ (x4+1x4)=10404−2=10402(x ^4+ \frac{1}{x^4} ) = 10404-2= 10402