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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? : Numeric Entry Question

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If x + y = 3 and x2 + y2 = 12, what is the value of 2xy? [#permalink]
If \(x + y = -3\) and \(x^2 + y^2 = 12\), what is the value of \(2xy\)?

The key here is to recognize that you are being asked for the value of \(2xy\) and also to note that we are given the value of \(x^2 + y^2\)

We know that \((x+y)^2 = x^2 + y^2 + 2xy\)

and therefore, \(x^2 + y^2 =(x+y)^2 - 2xy. \)

Thus,

\(x^2 + y^2 = 12\)

\((x+y)^2 - 2xy = 12.\)

\((-3)^2 - 2xy = 12\)

\(9 - 2xy = 12\)

\(- 2xy = 12 - 9\)

\(-2xy = 3\)

\(2xy = -3\)
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If x + y = 3 and x2 + y2 = 12, what is the value of 2xy? [#permalink]
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