# If X = 3 and Y = − 1, Find the Values of the Following Using in Identify: ( 3 X − X 3 ) ( X 2 9 + 9 X 2 + 1 ) - Mathematics

If x = 3 and y = − 1, find the values of the following using in identify:

$\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)$

#### Solution

In the given problem, we have to find the value of equation using identity

Given $\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)$

We shall use the identity  (a-b)(a^2 + ab + b^2) = a^3 - b^3

We can rearrange the  $\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)$as

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

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

$= \left( \frac{3}{x} \right) \times \left( \frac{3}{x} \right) \times \left( \frac{3}{x} \right) - \left( \frac{x}{3} \right) \times \left( \frac{x}{3} \right) \times \left( \frac{x}{3} \right)$

$= \frac{27}{x^3} - \frac{x^3}{27}$

Now substituting the value x=3, in 27/x^3 - x^3/27we get,

27/3^3 - 3^3/27

27/27 - 27/27

 = 0

Hence the Product value of  $\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)$ is 0.

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.4 | Q 2.2 | Page 24