If x^4+16/x^4=56,find the value of x-2/x
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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
I hope this will help you
(-:
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
I hope this will help you
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