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