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(a + b)^2 Expansion and Visualisation

If x2+1x2=2...

Question

If $x^{2} + \frac{1}{x^{2}} = 27$ , find the value of $x + \frac{1}{x}$ .

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Solution

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

$(x + \frac{1}{x})^{2} = 27 + 2$

$(x + \frac{1}{x})^{2} = 29$

$x + \frac{1}{x} = \pm \sqrt{29}$

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