If x − 1/x = −1, find the value of x2 + 1/x2

Question:

If $x-1 / x=-1$, find the value of $x^{2}+1 / x^{2}$

Solution:

We have, $x-1 / x=-1$

Now, $(x-1 / x)^{2}=x^{2}+(1 / x)^{2}-2 * x * 1 / x$

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

$\Rightarrow(-1)^{2}=x^{2}+1 / x^{2}-2[\therefore x-1 / x=-1]$

$\Rightarrow 2+1=x^{2}+1 / x^{2}$

$\Rightarrow x^{2}+1 / x^{2}=3$

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