If x-1-x-1- Find value of x2-1-x2

The correct option is D 3x 1/x = 1 Squaring both sides, We get, nbsp;(x 1/x )^2=( 1)^2 Using the identity: (a b)^2 = a^2 2ab +b^2 ⇒ x^2+(1/x)^2 2 × x×1/x= ...

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Byju's Answer

Standard VIII

Mathematics

Simplification of an Expression

If x-1/x=-1. ...

Question

If $x - \frac{1}{x} = - 1$ . Find value of $x^{2} + (\frac{1}{x})^{2}$ .

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Solution

The correct option is C $3$
$x - \frac{1}{x} = - 1$
Squaring both sides,
We get, $(x - \frac{1}{x})^{2} = (- 1)^{2}$
Using the identity: $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$\Rightarrow x^{2} + (\frac{1}{x})^{2} - 2 \times x \times \frac{1}{x} = 1$
$\Rightarrow x^{2} + (\frac{1}{x})^{2} - 2 = 1$
$\Rightarrow x^{2} + (\frac{1}{x})^{2} = 1 + 2 = 3$

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If x−1x=−1. Find value of x2+(1x)2.

The correct option is C 3x−1x=−1 Squaring both sides, We get, (x−1x)2=(−1)2 Using the identity: (a−b)2=a2−2ab+b2 ⇒x2+(1x)2−2×x×1x=1 ⇒x2+(1x)2−2=1 ⇒x2+(1x)2=1+2=3

If $x - \frac{1}{x} = - 1$ . Find value of $x^{2} + (\frac{1}{x})^{2}$ .