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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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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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Difficulty:   5% (low)

Question Stats: 86% (01:01) correct 14% (01:50) wrong based on 49 sessions

### HideShow timer Statistics [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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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.

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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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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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=>

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

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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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(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?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

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

$$A. 28$$
$$B. 39$$
$$C. 50$$
$$D. 61$$
$$E. 72$$

If we expand the expression (x + y)^2, we obtain x^2 + y^2 + 2xy. We can now evaluate the new expression by substituting the given values :

28 + 2 x 11 = 28 + 22 = 50

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?   [#permalink] 04 Feb 2019, 18:41
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# If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  