Question

If x^4+16/x^4=56,find the value of x-2/x

Answer 1

x⁴ + 16/x⁴ = 56

Adding 2[ x² × 4/x²]

x⁴ + 16/x⁴ + 2[ x² × 4/x²] = 56 + 2[ x² × 4/x²]



(x² + 4/x²)² = 56 + 2(4)

(x² + 4/x²)² = 56 + 8 = 64

x² + 4/x² = 8

Subtracting 2[x × 2/x]

x² + (2/x)² - 2 [ x× 2/x] = 8 - 2[ x × 2/x]

(x - 2/x)² = 8 - 2(2)

(x - 2/x)² = 8-4=4

x - 2/x = √4 = 2


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Answer 2

Step-by-step explanation:

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