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

Answer in Brief

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

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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^2`is 3 .

 

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APPEARS IN

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