Question

If x-1/x=-1, then find x^2+1/x^2

Answer 1

Answer:

$x^{2}+\frac{1}{x^{2}}=3$

Step-by-step explanation:

$x-\frac{1}{x}=-1\:--(1)$

$x^{2}+\frac{1}{x^{2}}\\=\left(x-\frac{1}{x}\right)^{2}+2\\=(-1)^{2}+2\\=1+2\\=3$

Therefore,

$x^{2}+\frac{1}{x^{2}}=3$

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Answer 2

The value of  $x^2+\dfrac{1}{x^2}$ is equal to 3.

Step-by-step explanation:

We are given with $x-\dfrac{1}{x}=-1\ .....(1)$

Squaring equation (1) on both sides such that,

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

Using $(a-b)^2=a^2+b^2-2ab$

So,

$x^2+\dfrac{1}{x^2}-2=1\\\\x^2+\dfrac{1}{x^2}=3$

So, the value of  $x^2+\dfrac{1}{x^2}$ is equal to 3.

Learn more,

Algebra

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