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Greatest Binomial Coefficients

Find x if ...

Question

Find $x$ if $\frac{1}{x^{2}} + \frac{1}{x} = 2$

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Solution

$\frac{1}{x^{2}} + \frac{1}{x} = 2 1 + x = 2 x^{2} 2 x^{2} - x - 1 = 0 2 x^{2} - 2 x + x - 1 = 0 2 x (x - 1) - 1 (x - 1) = 0 (2 x - 1) (x - 1) = 0 x = 1, \frac{1}{2}$

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x + 1 / x = 3

x^{2} + 1 / x^{2}

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{(x - \frac{1}{x})}^{2}

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