The number $x$ is $2$ more than the number $y$ . If the sum of the squares of $x$ and $y$ is $34$ ; find the product of $x$ and $y$ .

13

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4

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12

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15

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Solution

The correct option is D $15$
Given, $x = y + 2$ and $x^{2} + y^{2} = 34$
Now, $x = y + 2$
$=> x - y = 2$
Squaring both sides,
$=> (x - y)^{2} = 4$
$=> x^{2} + y^{2} - 2 x y = 4$
$=> 34 - 2 x y = 4$
$=> 2 x y = 34 - 4$
$=> x y = \frac{30}{2}$
$=> x y = 15$

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