Question

If x+1/x=-1 then find value of x square+1/x square

Answer 1

Answer:

$\color{red} \bold{\large{ {x}^{2} + \frac{1}{ {x}^{2} } = - 1}}$

Step-by-step explanation:

$\bold{given} \\ \\ \bold{x + \frac{1}{x} = - 1} \\ \\ \bold{squaring \: on \: both \: sides} \\ \\ \bold{ {(x + \frac{1}{x} )}^{2} = {( - 1)}^{2} } \\ \\ \bold{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 1} \\ \\ \bold{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 1} \\ \\ \bold{ {x}^{2} + \frac{1}{ {x}^{2} } = - 1} \\ \\ \large \color{blue}\bold{formula > = > {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy }$

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Answer 2

Step-by-step explanation:

x+1/x=1 (given)

on squaring above we have -

x^2+1/x^2+2=1^2

x^2+1/x^2+2=1

x square+1/x square= 1-2

x square+1/xsquare = -1