If x^4+1/x^4=119, find: x^2+1/x2 and x-1/x
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Answer:
Step-by-step explanation:
x⁴ + 1/x⁴ = 119.
But x⁴ + 1/x⁴ = (x² + 1/x²)² - 2
=> 119 = (x² + 1/x²)² - 2
=> (x² + 1/x²)² = 119 + 2 = 121
=> x² + 1/x² = √121 = 11
Similarly
x² + 1/x² = (x - 1/x)² + 2
=> 11 = (x - 1/x)² + 2
=> (x - 1/x)² = 11 - 2 = 9
=> x - 1/x = √9 = 3.
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