Question

x + 1 / x =4 find x raise to power 4 + 1/ x raise to power 4

Answer 1

Value of x⁴ + 1/x⁴ is 194.

Explanation :

Given:

• x + 1/x = 4

Squaring both sides,

⇒ (x + 1/x)² = 4²

or, x² + 2x(1/x) + 1/x² = 16

or , x² + 1/x² + 2 = 16

or, x² + 1/x² = 14

Again squaring both sides,

⇒ (x² + 1/x² )² = 14²

or, x⁴ + 2.x² (1/x² ) + 1/x⁴ = 196

or, x⁴ + 1/x⁴ + 2 = 196

or, x⁴ + 1/x⁴ = 194

∴ Value of x⁴ + 1/x⁴ is 194.

Answer 2

Given:

x + 1/x = 4

Squaring both sides,

⇒ (x + 1/x)² = 4²

or, x² + 2x(1/x) + 1/x² = 16

or , x² + 1/x² + 2 = 16

or, x² + 1/x² = 14

Again squaring both sides,

⇒ (x² + 1/x² )² = 14²

or, x⁴ + 2.x² (1/x² ) + 1/x⁴ = 196

or, x⁴ + 1/x⁴ + 2 = 196

or, x⁴ + 1/x⁴ = 194

∴ Value of x⁴ + 1/x⁴ is 194.