Evaluate $9 x^{2} + 25 y^{2} = 181 a n d x y = - 6$ find 3x + 5y = ?

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Solution

$9 x^{2} + 25 y^{2} = 181$ and $x y = - 6$

$3 x + 5 y = ?$

Use ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

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

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

$= 181 + 30 (- 6)$

$= 181 - 180 = 1$

Therefore,
$3 x + 5 y = \pm 1$

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Similar questions

If ${9 x}^{2} + {25 y}^{2} = 181$ and xy = - 6. Find the value of 3x + 5y

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