If x^2 + 1 /x^ 2 = 83, find the value of x3 - 1 /x ^3
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Answer:
±756
Step-by-step explanation:
(x - 1/x)² = x² + 1/x² - 2 = 83 - 2 = 81
⇒ x - 1/x = ±9
x³ - 1/x³
= (x³ - 3x²(1/x) + 3x(1/x²) - 1/x³) + 3(x - 1/x)
= (x - 1/x)³ + 3(x - 1/x)
= (x - 1/x)² (x - 1/x) + 3(x - 1/x)
= 81(x - 1/x) + 3(x - 1/x)
= 84(x - 1/x)
= ± 84 × 9
= ±756
Hope that helps
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