# If X − 1 X = 1 2 ,Then Write the Value of 4 X 2 + 4 X 2 - Mathematics

If $x - \frac{1}{x} = \frac{1}{2}$,then write the value of $4 x^2 + \frac{4}{x^2}$

#### Solution

We have to find the value of  4x^2 + 4/x^2

Given  x- 1/x = 1/2

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

Here  a= x,b= 1/x

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

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

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

By substituting the value of  x - 1/x = 1/x we get

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

By transposing – 2 to left hand side we get

1/4 +2 = x^2 +1/x^2

By taking least common multiply we get

1/4+2/1 = x^2 + 1/x^2

1/4 +2/1 xx 4/4 = x^2 + 1/x^2

1/4 +8/4 = x^2 +1/x^2

(1+8)/4 = x^2 + 1/x^2

(+9)/4 = x^2 + 1/x^2

By multiplying 4 on both sides we get

4 xx 9/4 = 4x^2 + 4 xx 1/x^2

4 xx 9/4 = 4x^2 + 4/x^2

9 =4x^2 + 4/x^2

Hence the value of  4x^2 + 4/x^2 is 9.

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.5 | Q 5 | Page 29