Question

if x+1/x = -1 find the value of x square + 1/xsquare​

Answer 1

Answer:

HOW TO SOLVE?

$x + \frac{1}{x} = - 1 \\ {x}^{2} + \frac{1}{ {x}^{2} } = {?}$

Let us see,

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

According to question,

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

The answer is -1.

HOPE IT HELPS YOU!!!

HAVE A NICE DAY!!!