Question

If ( x -1/x) = 5, find the values of

a) (x² + 1/x²)​

Answer 1

Step-by-step explanation:

WE KNOW THAT

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

SO,

${x}^{2} + \frac{1}{ {x}^{2} } = {5}^{2} + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7$