Question

If x square + 1/x square = 38, find the value of x to the power of 4 +1/ x to the power of 4

Answer 1

Answer:

x⁴ + (1/x⁴) = 1442

Step-by-step explanation:

We have,

x² + (1/x²) = 38

Squaring both sides,

(x² + (1/x²))² = 38²

We know that,

(a + b)² = a² + 2ab + b²

Then,

(x² + (1/x²))² = 38²

(x²)² + 2(x²)(1/x²) + (1/x²)² = 1444

x⁴ + 2 + (1/x⁴) = 1444

x⁴ + (1/x⁴) = 1444 - 2

x⁴ + (1/x⁴) = 1442

Hence,

x⁴ + (1/x⁴) = 1442

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