Find the Value of the Following Expression: 81x2 + 16y2 − 72xy, When X = 2 3 and Y = 3 4 - Mathematics

Find the value of the following expression:  81x2 + 16y2 − 72xy, when $x = \frac{2}{3}$ and  $y = \frac{3}{4}$

Solution

Let us consider the following expression: $81 x^2 + 16 y^2 - 72xy$

Now

$81 x^2 + 16 y^2 - 72xy = \left( 9x - 4y \right)^2$         (Using identity $\left( a + b \right)^2 = a^2 - 2ab + b^2$)

$\Rightarrow 81 x^2 + 16 y^2 - 72xy = \left[ 9\left( \frac{2}{3} \right) - 4\left( \frac{3}{4} \right) \right]^2 (\text { Substituting } x = \frac{2}{3}\text { and y } = \frac{3}{4})$

$\Rightarrow 81 x^2 + 16 y^2 - 72xy = \left[ 6 - 3 \right]^2$

$\Rightarrow 81 x^2 + 16 y^2 - 72xy = 3^2$

$\Rightarrow 81 x^2 + 16 y^2 - 72xy = 9$

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RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 13.3 | Page 44