X+1/x=root 2 find value of x²+1/x²

1.	X+1/x=root 2 find value of x²+1/x²
Answer» $Given \: x + \frac{1}{x} = \sqrt{2} \: --(1)$ /* 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., $\red { The \: value \:of \: x^{2} + \frac{1}{x^{2}} }\green{= 0}$ •••♪

Answer»

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