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Expansion of (x-y)^2

Two numbers d...

Question

Two numbers differ by 5, The sum of square of these numbers is 97. Find the product of the numbers.

A

24

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B

66

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C

14

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D

36

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Solution

The correct option is D
36

$x^{2} + y^{2} = 97$

$(x - y) = 5$

square on both sides.

$x^{2} + y^{2} - 2 x y = 25$

$x^{2} + y^{2} - 2 x y = 25$ .

We know that $x^{2} + y^{2} = 97$ .

Hence $97 - 2 x y = 25$

$\Rightarrow 97 - 25 = 2 x y$

$\Rightarrow 72 = 2 x y$

$\Rightarrow x y = \frac{72}{2} = 36$

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