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(a-b)^2 Expansion and Visualisation

If x+1x=6, ...

Question

If $x + \frac{1}{x} = 6$ , find $x^{2} + \frac{1}{x^{2}}$ .

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Solution

$x + \frac{1}{x} = 6$

$(x + \frac{1}{x})^{2} = 36$

$x^{2} + \frac{1}{x^{2}} + 2 = 36$

$x^{2} + \frac{1}{x^{2}} = 34$

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