An algebra problem by A Former Brilliant Member

Algebra Level 1

If x + y = 6 x+y=6 and x 2 + y 2 = 27 x^2+y^2=27 , find x y xy .


The answer is 4.5.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

We know that

( x + y ) 2 = x 2 + 2 x y + y 2 (x+y)^2=x^2+2xy+y^2

Substituting, we have

6 2 = 27 + 2 x y 6^2=27+2xy

36 = 27 + 2 x y 36=27+2xy

36 − 27 = 2 x y 36-27=2xy

9 = 2 x y 9=2xy

9 2 = x y \dfrac{9}{2}=xy

4.5 = x y \boxed{4.5=xy}

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