Question

If x +1 / x= 4, then Find The Value Of --> x4 +1 / x4

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 4.

As we know that,

We can write equation as,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (4)².

⇒ x² + 1/x² + 2(x)(1/x) = 16.

⇒ x² + 1/x² + 2 = 16.

⇒ x² + 1/x² = 16 - 2.

⇒ x² + 1/x² = 14.

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

⇒ (x² + 1/x²)² = (14)².

⇒ x⁴ + 1/x⁴ + 2(x²)(1/x²) = 196.

⇒ x⁴ + 1/x⁴ + 2 = 196.

⇒ x⁴ + 1/x⁴ = 196 - 2.

⇒ x⁴ + 1/x⁴ = 194.

Answer 2

Answer:

Step-by-step explanation:

x^4+1/x^4

(x^2+1/x^2) = (x^4+1/x^4) + 2

(x^4+1/x^4) = (x^2 + 1/x^2) -2

(x^4+1/x^4) = (14)^2 - 2

(x^4+1/x^4) = 196 - 2

(x^4+1/x^4) = 194