If $3 x + 5 y = 11$ and $x y = 2$ , find the value of $9 x^{2} + 25 y^{2}$ .

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Solution

Given: $3 x + 5 y = 11$ , $x y = 2$

To find $9 x^{2} + 25 y^{2}$

$3 x + 5 y = 11$
Squaring both sides, we get
$(3 x + 5 y)^{2} = (11)^{2}$

$9 x^{2} + 25 y^{2} + 30 x y = 121$

$9 x^{2} + 25 y^{2} + 30 \times 2 = 121$ $(∵ x y = 2)$

$9 x^{2} + 25 y^{2} + 60 = 121$
$9 x^{2} + 25 y^{2} = 121 - 60$

$9 x^{2} + 25 y^{2} = 61$

$∴ 9 x^{2} + 25 y^{2} = 61$ .

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