Question

if x⁴+1/x⁴ =119, find x²+1/x² and x +1/x
Please answer the question with explanation ​

Answer 1

EXPLANATION.

⇒ If x⁴ + 1/x⁴ = 119.

As we know that,

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2(x²)(1/x²).

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2.

Put the value of (x⁴ + 1/x⁴) = 119 in equation, we get.

⇒ (x² + 1/x²)² = 119 + 2.

⇒ (x² + 1/x²)² = 121.

⇒ (x² + 1/x²) = √121.

⇒ (x² + 1/x²) = 11.

As we know that,

⇒ (x + 1/x)² = x² + 1/x² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

Put the value of (x² + 1/x²) = 11 in equation, we get.

⇒ (x + 1/x)² = 11 + 2.

⇒ (x + 1/x)² = 13.

⇒ (x + 1/x) = √13.

Value of (1) = x² + 1/x² = 11  and  (2) = x + 1/x = √13.

Answer 2

Answer:

Given :

• x⁴ + 1/x⁴ = 119

To find :

• value of x²+1/x² and x +1/x

Solution :

(i) We know that,

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2(x²)(1/x²).

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2.

Put the value of (x⁴ + 1/x⁴) = 119 in equation, we get.

⇒ (x² + 1/x²)² = 119 + 2.

⇒ (x² + 1/x²)² = 121.

⇒ (x² + 1/x²) = √121.

⇒ (x² + 1/x²) = 11.

(ii) we know that,

⇒ (x + 1/x)² = x² + 1/x² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

Put the value of (x² + 1/x²) = 11 in equation, we get.

⇒ (x + 1/x)² = 11 + 2.

⇒ (x + 1/x)² = 13.

⇒ (x + 1/x) = √13.

• So, the value of (i) = x² + 1/x² = 11  and  (ii) = x + 1/x = √13.

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