Question

If 9x*2 +25y*2= 181 and xy = -6 , find the value of 3x + 5y.

Answer 1

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${(3x + 5y)}^{2} = {(3x)}^{2} + {(5y)}^{2} + 2 \times 3x \times 5y$

$= {9x}^{2} + {25y}^{2} + 30xy$

$= 181 - 30 \times 6 \: \: \: \: \: \: \: \: \: \: \: (values \: are \: \\ given \: in \: the \: question)$

$= 181 - 180 \\ = 1$

${(3x + 5y)}^{2} = 1 \\ 3x + 5y = \sqrt{1} = 1$

——> 3x + 5y ≈ 1

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