Question

If x- 1\x=-2, find the value of x^2 + 1/x^2

Answer 1

$x - \frac{1}{x} = - 2$

Square on both sides,

${(x - \frac{1}{x}) }^{2} = {( - 2)}^{2} \\ \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } - 2(x \times \frac{1}{x} ) = 4 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 4 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } = 4 + 2 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } = 6$

Answer 2

Answer:

x - \frac{1}{x} = - 2

Square on both sides,

{(x - \frac{1}{x}) }^{2} = {( - 2)}^{2} \\ \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } - 2(x \times \frac{1}{x} ) = 4 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 4 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } = 4 + 2 \\ \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } = 6

Step-by-step explanation: