Question

x+1/x=root 2 find value of x²+1/x²

Answer 1

$Given \: x + \frac{1}{x} = \sqrt{2} \: --(1)$

/* On squaring both sides of equation (1), we get*/

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

$\implies x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} = 2$

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

$\implies x^{2} + \frac{1}{x^{2}} = 2 - 2$

$\implies x^{2} + \frac{1}{x^{2}} = 0$

Therefore.,

$\red { The \: value \:of \: x^{2} + \frac{1}{x^{2}} }\green{= 0}$

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