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If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?

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Math Revolution GMAT Instructor
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If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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New post 25 Dec 2018, 01:08
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[Math Revolution GMAT math practice question]

If \(x^2+y^2=28\) and \(xy=11\), what is the value of \((x+y)^2\)?

\(A. 28\)
\(B. 39\)
\(C. 50\)
\(D. 61\)
\(E. 72\)

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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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New post 25 Dec 2018, 05:46
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2+y^2=28\) and \(xy=11\), what is the value of \((x+y)^2\)?

\(A. 28\)
\(B. 39\)
\(C. 50\)
\(D. 61\)
\(E. 72\)



\(( x + y)^2\)
=\(x^2 + 2xy + y^2\)
= 28 + 2.11 = 50.

C is the answer.
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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New post 25 Dec 2018, 06:08
If we expand (x+y)² we end up at x² + 2xy + y² (Bionomical Theorem)

Notice that we were already provided with the solutions to the respective parts of the equation:

x² + y² = 28
xy = 11

Thus, we can plug those values into our equation: 28 + 2(11) = 50
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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New post 27 Dec 2018, 01:18
=>

\((x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 2*11 = 28 + 22 = 50.\)

Therefore, the answer is C.
Answer: C
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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New post 27 Dec 2018, 10:04
(x+y)^2 = x^2+ y^2 + 2xy
substitute the values
28+22= 50 (C)
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? &nbs [#permalink] 27 Dec 2018, 10:04
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