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Question
If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2
Solution
We have:
\[\left( 3x + 5y \right)^2 = \left( 3x \right)^2 + 2\left( 3x \right)\left( 5y \right) + \left( 5y \right)^2 \]
\[ \Rightarrow \left( 3x + 5y \right)^2 = 9 x^2 + 30xy + 25 y^2 \]
\[ \Rightarrow 9 x^2 + 25 y^2 = \left( 3x + 5y \right)^2 - 30xy\]
\[\Rightarrow 9 x^2 + 25 y^2 = {11}^2 - 30 \times 2\] (\[\because\] \[3x + 5y = 11 \text { and } xy = 2\])
\[\Rightarrow 9 x^2 + 25 y^2 = 121 - 60\]
\[ \Rightarrow 9 x^2 + 25 y^2 = 61\]
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