Question

$if x-\frac{1}{x} =2... find,, x^4+\frac{1}{x^4}$

Answer 1

EXPLANATION.

⇒ (x - 1/x) = 2.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x - 1/x)² = (2)².

⇒ x² + 1/x² - 2(x)(1/x) = 4.

⇒ x² + 1/x² - 2 = 4.

⇒ x² + 1/x² = 4 + 2.

⇒ x² + 1/x² = 6.

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

⇒ [x² + 1/x²]² = (6)².

⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = 36.

⇒ x⁴ + 1/x⁴ + 2 = 36.

⇒ x⁴ + 1/x⁴ = 36 - 2.

⇒ x⁴ + 1/x⁴ = 34.