Question

If x-1/x-8 find the value of x+2+1/x^2

Answer 1

$\star\:\:\bf\large\underline\blue{Question:-}$

• If $x - \frac{1}{x} = 8$, find the value of ${x}^{2} + \frac{1}{ {x}^{2} }$

$\star\:\:\bf\large\underline\blue{Solution:-}$

$x - \frac{1}{x} = 8$

Squaring both side, we get,

${(x - \frac{1}{x}) }^{2} = {8}^{2}$

$\implies {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times \cancel{x} \times \frac{1}{ \cancel{x}} = 64$

$\implies {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 64$

$\implies {x}^{2} + \frac{1}{ {x}^{2} } = 64 - 2$

$\implies {x}^{2} + \frac{1}{ {x}^{2} } = 62$

$\star\:\:\bf\large\underline\blue{Answer:-}$

• ${x}^{2} + \frac{1}{ {x}^{2} } = 62$

Answer 2

The value of x²+1/x² will be 62.

Calculations not included.