If x + = 7, then the value of x⁶ + is:

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 3)

Answer 1

Given:

x + 1/x = 7

Formula used:

If x + 1/x = n

then, x ² + 1/x² = n² - 2

And (x³ + y³) = n³ - 3n

Calculation:

x + 1/x = 7

⇒ x² + 1/x² = 7² - 2

⇒ x² + 1/x² = 47

Cubing both side we get

⇒ (x2 + 1/x2)³ = 47³

⇒ x⁶ + 1/x⁶ + 3 (x2 × 1/x2) (x2 + 1/x2) = 47³

⇒ x6 + 1/x6 + 3 × 1 × 47 = 473

⇒ x6 + 1/x6 = 473 - 3 × 47

⇒ x 6 + 1/x 6 = 103823 - 141

⇒ x 6 + 1/x 6 = 103682

∴ The value of x 6 + 1/x 6 is 103682.