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Algebraic Identities

If x + y = 3 ...

Question

If $x + y = 3$ and $x^{2} + y^{2} = 5$ , then find xy.

A

3

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B

5

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C

2

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D

1

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Solution

The correct option is C 2
$\Rightarrow (x + y (^{2} = x^{2} + y^{2} + 2 x y$
$\Rightarrow (3)^{2} = 5 + 2 x y$
$\Rightarrow 4 = 2 x y$
$\Rightarrow x y = 2$

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