Question

Find x+1/x,if square+1/x square=62

Answer 1

Step-by-step explanation:

It is given That,

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

Now ,

By Cross Multiplying,

We get,

${x}^{2} + 1 = 62 {x}^{2}$

$1 = 62 {x}^{2} - {x}^{2}$

$1 = 61 {x}^{2}$

$\frac{1}{61} = {x}^{2}$

$x = \frac{ + }{} \frac{1}{ \sqrt{61} }$

Now ,

We Have To Find ,

$\frac{x + 1}{x}$

Case 1:

Put

$x = \frac{1}{ \sqrt{61} }$

we get,

$\frac{ \frac{1}{ \sqrt{61} } + 1 }{ \frac{1}{ \sqrt{61} } }$

$\frac{ \frac{1 + \sqrt{61} }{ \sqrt{61} } }{ \frac{1}{ \sqrt{61} } }$

$\frac{x + 1}{x} = 1 + \sqrt{61}$

Case 2:

Put

$x = - \frac{ 1}{ \sqrt{61} }$

$\frac{ \frac{ - 1 + \sqrt{61} }{ \sqrt{61} } } { \frac{ - 1}{ \sqrt{61} } }$

$\frac{x + 1}{x} = \frac{ - 1 + \sqrt{61} }{ - 1}$

$\frac{x + 1}{x} = - ( - 1 + \sqrt{61)}$

$\frac{x + 1}{x} = 1 - \sqrt{61}$

Hence Solveddd....

Hope it Helpsss,