if-x-2-1-x-2-98-find-x-3-1-x-3-

Question Number 26227 by ktomboy1992 last updated on 23/Dec/17

if x^{2} + \frac{1}{x^{2}} = 98 find x^{3} + \frac{1}{x^{3}}

Answered by $@ty@m last updated on 22/Dec/17

x^{2} + \frac{1}{x^{2}} = {(x + \frac{1}{x})}^{2} - 2 = 98

\Rightarrow {(x + \frac{1}{x})}^{2} = 100

\Rightarrow x + \frac{1}{x} = 10

{(x + \frac{1}{x})}^{3} = x^{3} + \frac{1}{x^{3}} + 3 (x + \frac{1}{x})

\Rightarrow 1000 = x^{3} + \frac{1}{x^{3}} + 30

\Rightarrow x^{3} + \frac{1}{x^{3}} = 970

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