If \(\rm\left(x + \frac{1}{x}\right)\) = 2√2, what is the value of \(\rm\left(x^{6}+\frac{1}{x^{6}}\right)\)?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 2)

Answer 1

Given:

x + 1/x = 2√2

Formula used:

If x + 1/x = n

then, x2 + 1/x2 = n2 - 2

And (a + b)3 = a3 + b3 + 3ab (a + b)

Calculation:

x + 1/x = 2√2

⇒ x2 + 1/x2 = (2√2)2 - 2

⇒ x2 + 1/x2 = 6

Cubing both side we get

⇒ (x2 + 1/x2)3 = 63

⇒ x6 + 1/x6 + 3 (x2 × 1/x2) (x2 + 1/x2) = 63

⇒ x6 + 1/x6 + 3 × 1 × 6 = 63

⇒ x6 + 1/x6 = 63 - 3 × 6

⇒ x6 + 1/x6 = 216 - 18

⇒ x6 + 1/x6 = 198

∴ The value of x6 + 1/x6 is 198.