Question

If (x - 1/x ) = 12 , find the value of (x² + 1/x² )

Answer 1

$\huge\pink{\bf{\underline{Answer:-}}}$

$x - \frac{1}{x} = 12 \\ ⟹ (x + \frac{1}{x} )^{2} = (12)^{2} \\ ⟹ {x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 144 \\ ⟹ {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 144 \\ ⟹ {x}^{2} + \frac{1}{ {x}^{2} } = 144 - 2 \\ ⟹ {x}^{2} + \frac{1}{ {x}^{2} } = 142 \\ \\ \purple{\bf{\boxed{∴\: the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } \: is \: 142.}}}</p><p></p><p>$

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