Question

if x-1/x=3find the values of x²+1/x²and x⁴+1/x⁴.​

Answer 1

EXPLANATION.

⇒ x - 1/x = 3.

As we know that,

⇒ (a - b)² = a² + b² - 2ab.

Using this formula on equation, we get.

Squaring on both sides, we get.

⇒ (x - 1/x)² = (3)².

⇒ (x² + 1/x² - 2(x)(1/x)) = 9.

⇒ (x² + 1/x² - 2) = 9.

⇒ (x² + 1/x²) = 9 + 2.

⇒ (x² + 1/x²) = 11.

Again, squaring on both sides, we get.

⇒ (x² + 1/x²)² = (11)².

⇒ (x⁴ + 1/x⁴ + 2(x⁴)(1/x⁴) = 121.

⇒ (x⁴ + 1/x⁴ + 2) = 121.

⇒ (x⁴ + 1/x⁴) = 121 - 2.

⇒ (x⁴ + 1/x⁴) = 119.

Value of (x² + 1/x²) = 11.

Value of (x⁴ + 1/x⁴) = 119.

Answer 2

Appropriate Question

• if x-1/x=3find the values of x²+1/x²and x⁴+1/x⁴.

☯Solution ☯

::==> x^2+1/x^2=(x-1/x)^2+2x.1/x

=(3)^2+2=9+2=11

::==> x^4+1/x^4=(x^2+1/x^2)^2-2x^2.1/x^2

=(11)^2-2=121-2=119