# P If X − 1 X = − 1 Find the Value of X 2 + 1 X 2 - Mathematics

If $x - \frac{1}{x} = - 1$  find the value of  $x^2 + \frac{1}{x^2}$

#### Solution

In the given problem, we have to find x^2 + 1/x^2

Given  (x-1/x)=-1

On squaring both sides we get,

(x-1/x)^2=(-1)^2

We shall use the identity  (x-y )^2 = x^2 - 2xy + y

x^2 +1/x^2 - 2 xx x xx 1/x =- 1 xx -1

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

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

x^2+1/x^2 =3

Hence the value of  x^2 +1/x^2is 3 .

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.1 | Q 5 | Page 7