If $5 x - 2 y = 7$ and $x y = 2$ .find the value of $(5 x + 2 y)^{2}$ .

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Solution

Consider the given equation,

$5 x - 2 y = 7$ and $x y = 2$

We have to find ${(5 x + 2 y)}^{2} = ?$

Now,

${(5 x - 2 y)}^{2} = 25 x^{2} + 4 y^{2} - 20 x y$

$7^{2} = 25 x^{2} + 4 y^{2} - 20 \times 2$

$25 x^{2} + 4 y^{2} = 89$

Now,

${(5 x + 2 y)}^{2} = 25 x^{2} + 4 y^{2} - 20 x y$

${(5 x + 2 y)}^{2} = 89 - 20 \times 2$

${(5 x + 2 y)}^{2} = 49$

Hence, this is the answer.

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