Suppose

*a*and

*b*are real numbers and (

*a*+

*b*)^2 = 56 and

*a*^2 +

*b*^2 = 18. What is the value of

*ab*?

The key to the problem is knowing that when you expand (

*a*+

*b*)^2, you will have

*a*^2 +

*b*^2 and

*ab*as part of the expansion, which makes the problem easy.

(

*a*+

*b*)^2 =

*a*^2 + 2

*ab*+

*b*^2

Now substitute and solve for

*ab.*

56 = 18 + 2

38 = 2

*ab*

19 =

*ab*

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