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If x^2+y^2=2xy, then (x-y)^2=?

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Math Revolution GMAT Instructor
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If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 03 Aug 2018, 01:13
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C
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[Math Revolution GMAT math practice question]

If \(x^2+y^2=2xy\), then \((x-y)^2\)=?

\(A. x^2\)
\(B. y^2\)
\(C. 0\)
\(D. 1\)
\(E. 2\)

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Re: If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 03 Aug 2018, 01:18
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2+y^2=2xy\), then \((x-y)^2\)=?

\(A. x^2\)
\(B. y^2\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


Simplify the question:
\((x-y)^2\)=?
\(x^2 - 2xy + y^2\)=?

It is given that,
\(x^2+y^2=2xy\)
\(x^2-2xy+y^2=0\)

Hence the answer is 0. Therefore Option C is correct.

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Re: If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 03 Aug 2018, 05:48
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2+y^2=2xy\), then \((x-y)^2\)=?

\(A. x^2\)
\(B. y^2\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


APPROACH #1: Algebra
Given: x² + y² = 2xy
Subtract 2xy from both sides: x² - 2xy + y² = 0 (this should look familiar....it's a special product)
Factor left side: (x - y)(x - y) = 0
In other words, (x - y)² = 0

Answer: C

Cheers,
Brent
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Re: If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 03 Aug 2018, 05:53
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2+y^2=2xy\), then \((x-y)^2\)=?

\(A. x^2\)
\(B. y^2\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


APPROACH #2 - Plug in numbers
First find values of x and y that satisfy the given information (x² + y² = 2xy)
Notice that, when x = 1 and y = 1, the equation, x² + y² = 2xy, holds true.

We want to find the value of (x - y)²
Plug in x = 1 and y = 1 to get: (x - y)² = (1 - 1
= 0²
= 0

Answer: C

Cheers,
Brent
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Re: If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 03 Aug 2018, 08:11
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2+y^2=2xy\), then \((x-y)^2\)=?

\(A. x^2\)
\(B. y^2\)
\(C. 0\)
\(D. 1\)
\(E. 2\)

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

Or,\(x^2+y^2 - 2xy = 0\)

Or,\((x - y)^2= 0\), Answer must be (C) 0
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Re: If x^2+y^2=2xy, then (x-y)^2=?  [#permalink]

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New post 05 Aug 2018, 18:07
=>
\(x^2+y^2=2xy\)
\(=> x^2 - 2xy + y^2 = 0\)
\(=> ( x – y )^2 = 0\)

Therefore, the answer is C.
Answer: C
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Re: If x^2+y^2=2xy, then (x-y)^2=? &nbs [#permalink] 05 Aug 2018, 18:07
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