Question

If x-1/x = 9, find the value of x²+1/x² (Using a suitable identity).​

Answer 1

Answer:

83

Step-by-step explanation:

x-1/x=9

(x-1/x)^2=81

x^2+(1/x)^2=81+2=83

Answer 2

Given,

${ \boxed{ \huge{ \mathtt{x - \frac{1}{x} = 9}}}}$

Now,

$= > { \boxed { \huge{ \mathbf{ {(x - \frac{1}{x} )}^{2} = {(9)}^{2} }}}} \\ \\ = > { \boxed{ \huge{ \mathtt{ {x}^{2} + \frac{1}{ {x}^{2} } - 2(x)(\frac{1}{x}) = 81 }}}}\\\\ = > { \boxed{ \huge{ \mathtt{ {x}^{2} + \frac{1}{ {x}^{2} } - 2= 81}}}}\\ \\ = > { \boxed{ \huge{ \mathtt{ {x}^{2} + \frac{1}{ {x}^{2} } = 81 + 2 }}}} \\ \\ = > { \huge{ \boxed{ \huge{ \mathtt{ { \red{ {x}^{2} + \frac{1}{ {x}^{2} } =83 }}}}}}}$