Question

please step by step <br />$if \: x - \frac{1}{x} = 3 \: then \: find \: the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} }$<br />$if \: x - \frac{1}{x} = 3 \: then \: find \: the \: value \: of \: {x}^{2} \times + \frac{1}{ {x}^{2} }$<br />​

Answer 1

Answer :

x² + 1/x² = 11

Solution :

• Given : x - 1/x = 3
• To find : x² + 1/x² = ?

We have ,

x - 1/x = 3

Now ,

Squaring both the sides , we get ;

=> (x - 1/x)² = 3²

=> x² + (1/x)² - 2•x•(1/x) = 9

=> x² + 1/x² - 2 = 9

=> x² + 1/x² = 9 + 2

=> x² + 1/x² = 11

Hence ,

x² + 1/x² = 11