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

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by Max@Math Revolution » Fri Aug 03, 2018 12:56 am

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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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by Brent@GMATPrepNow » Fri Aug 03, 2018 5:41 am
Max@Math Revolution wrote:
If x² + y² = 2xy, then (x - y)² = ?
A. x²
B. y²
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

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Brent
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by Brent@GMATPrepNow » Fri Aug 03, 2018 5:46 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x² + y² = 2xy, then (x - y)² = ?
A. x²
B. y²
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)²
= 0²
= 0

Answer: C

Cheers,
Brent
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by Max@Math Revolution » Sun Aug 05, 2018 5:55 pm
=>
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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