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Find the Value of the Following Expression: 64x2 + 81y2 + 144xy, When X = 11 and Y = 4 3 - Mathematics

Answer in Brief

Find the value of the following expression:  64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]

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Solution

 Let us consider the following expression: \[64 x^2 + 81 y^2 + 144xy\] 

Now \[64 x^2 + 81 y^2 + 144xy = \left( 8x + 9y \right)^2\]          (Using identity \[\left( a + b \right)^2 = a^2 + 2ab + b^2\])

\[\Rightarrow 64 x^2 + 81 y^2 + 144xy = \left[ 8\left( 11 \right) + 9\left( \frac{4}{3} \right) \right]^2 (\text { Substituting  x = 11 and y } = \frac{4}{3})\]

\[ \Rightarrow 64 x^2 + 81 y^2 + 144xy = \left[ 88 + 12 \right]^2 \]

\[ \Rightarrow 64 x^2 + 81 y^2 + 144xy = {100}^2 \]

\[ \Rightarrow 64 x^2 + 81 y^2 + 144xy = 10000\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 13.2 | Page 44
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