# If 3 X + 2 X = 7 , Then ( 9 X 2 − 4 X 2 ) = - Mathematics

MCQ

If  $3x + \frac{2}{x} = 7$ , then $\left( 9 x^2 - \frac{4}{x^2} \right) =$

• 25

• 35

• 49

• 30

#### Solution

We have to find the value of  (9x^2 - 4/x^2)

Given  3x +2/x = 7

Using identity  (a+b)^2 = a^2 +b^2 +2ab  we get,

Here  a = 3x ,b= 2/x

(3x +2/x )^2 = (3x)^2 + 2 xx 3x xx 2/x + (2/x)^2

Substituting  3x + 2/x = 7 we get,

(7)^2 = 9x^2 + 2 xx 3 xx x xx 2/x +(2/x)^2

49 = 9x^2 + 12 +4/x^2

By transposing  + 12  left hand side we get,

49 - 12 = 9x^2 +4/x^2

37 = 9x^2 + 4/ x^2

Again using identity   (a-b)^2 = a^2 - 2ab +b^2 we get,

(3x - 2/x)^2 = (3x )^2 - 2 xx 3x xx 2/x + (2/x)^2

(3x- 2/x)^2=(9x)^2 + 4/x^2 - 12

Substituting  (9x)^2 + 4/x^2 = 37 we get

(3x - 2/x)^2 = 37 - 12

(3x - 2/x)^2 = 25

(3x - 2/x)(3x - 2/x) = 5 xx 5

3x - 2/x = 5

Using identity  (x + y)( x - y )we get

Here  x= 3x,y = 2/x

(3x)^2 - (2/x)^2 = (3x + 2/x)(3x - 2/x)

Substituting  3x +2/x = 7,3x - 2/x = 5 we get,

9x^2 - 4/x^2 = 7 xx 5 

9x^2 - 4/x^2 = 35

The value of  9x^2 - 4/x^2`is 35.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Q 18 | Page 31