Question

If x+1/x=8, then the value of x^4+1/x^4 is equal to​

Answer 1

Step-by-step explanation:

x²+1/x²+2=64

x²+1/x²=62

x⁴+1/x⁴+2=3844

x⁴+1/x⁴=3842

Answer 2

EXPLANATION.

⇒ (x + 1/x) = 8.

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

Using this formula in this question, we get.

Squaring on both sides of the expression, we get.

⇒ (x + 1/x)² = (8)².

⇒ (x)² + (1/x)² + 2(x)(1/x) = 64.

⇒ x² + 1/x² + 2 = 64.

⇒ x² + 1/x² = 64 - 2.

⇒ x² + 1/x² = 62.

Again squaring on both sides of the expression, we get.

⇒ (x² + 1/x²)² = (62)².

⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = 3844.

⇒ x⁴ + 1/x⁴ + 2 = 3844.

⇒ x⁴ + 1/x⁴ = 3844 - 2.

⇒ x⁴ + 1/x⁴ = 3842.

∴ The value of x⁴ + 1/x⁴ is 3842.