[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
If x^2+y^2=2xy, then (x-y)^2=?
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- Max@Math Revolution
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Your Answer
A
B
C
D
E
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APPROACH #1: AlgebraMax@Math Revolution wrote:
If x² + y² = 2xy, then (x - y)² = ?
A. x²
B. y²
C. 0
D. 1
E. 2
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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- Brent@GMATPrepNow
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APPROACH #2 - Plug in numbersMax@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
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
- Max@Math Revolution
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=>
x^2+y^2=2xy
=> x^2 - 2xy + y^2 = 0
=> ( x - y )^2 = 0
Therefore, the answer is C.
Answer: C
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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[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
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