Question

if (x^4+1/x^4)is equal to 322,then the value of (x-1/x)will be​

Answer 1

Answer:

4

Step-by-step explanation:

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Answer 2

EXPLANATION.

(x⁴ + 1/x⁴) = 322.

To find the value of (x - 1/x).

As we know that,

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

⇒ (x² + 1/x²)² = 322 + 2.

⇒ (x² + 1/x²)² = 324.

⇒ (x² + 1/x²) = √324.

⇒ (x² + 1/x²) = 18.

As we know that,

Formula of = (a² + b²) = (a - b)² + 2ab.

⇒ (x - 1/x)² + 2(x)(1/x) = 18.

⇒ (x - 1/x)² + 2 = 18.

⇒ (x - 1/x)² = 18 - 2.

⇒ (x - 1/x)² = 16.

⇒ (x - 1/x) = √16.

⇒ (x - 1/x) = ± 4.