Question

if x-1/x=5 then find the valu of x2+1/x2​

Answer 1

Solution:-

Given:-

$\rm \: x - \dfrac{1}{x} = 5 \: \:$

To find Value of

$\rm \: {x}^{2} + \dfrac{1}{x {}^{2} }$

Now take

$\rm \: x - \dfrac{1}{x} = 5 \: \:$

Squaring on both side

$\rm \: \bigg(x - \dfrac{1}{x} \bigg) {}^{2} = {5}^{2}$

Using this identity

$\rm \: (a - b) {}^{2} = {a}^{2} + {b}^{2} - 2ab$

We get

$\rm \: {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 \times x \times \dfrac{1}{x} = 25$

$\rm \: {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 \times \not{x }\times \dfrac{1}{ \not{x}} = 25$

$\rm \: x {}^{2} + \dfrac{1}{ {x}^{2} } - 2 = 25$

$\rm \: x {}^{2} + \dfrac{1}{ {x}^{2} } = 25 + 2$

$\rm {x}^{2} + \dfrac{1}{ {x}^{2} } = 27$

So value of x² + 1 / x² = 27