# Mark the Correct Alternative in Each of the Following: - Mathematics

MCQ

Mark the correct alternative in each of the following:

If $x + \frac{1}{x} = 5$ then $x^2 + \frac{1}{x^2} =$

• 25

• 10

• 23

• 27

#### Solution

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

Given  x+ 1/x = 5

We shall use the identity (a+b)^2 = a^2 + b^2 + 2ab

Here put x+1/x = 5

(x+1/x)^2 = x^2 +1/x^2 +2 (x xx 1/x)

(5)^2 = x^2 + 1/x^2 +2 (x xx 1/x)

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

25 - 2 = x^2 +1/x^2

23 = x^2 + 1/x^2

Hence the value of   x^2 + 1/x^2 is 23.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Q 1 | Page 30