Question

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

Answer 1

 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 \[\left( a + b \right)^2 = a^2 + 2ab + b^2\])

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

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

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

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