If $3 x + 4 y = 16$ and $x y = 4$ ; find the value of $9 x^{2} + 16 y^{2}$ .

160

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130

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180

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156

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Solution

The correct option is A $160$
$3 x + 4 y = 16$
Squaring both sides
$=> (3 x + 4 y)^{2} = 256$
$=> 9 x^{2} + 16 y^{2} + 2 (3 x) (4 y) = 256$
$=> 9 x^{2} + 16 y^{2} + 24 x y = 256$
$=> 9 x^{2} + 16 y^{2} = 256 - 24 \times 4$
$=> 9 x^{2} + 16 y^{2} = 256 - 96$
$=> 9 x^{2} + 16 y^{2} = 160$

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