Bunuel wrote:
If \((x − y)^2 = x^2 + y^2\), then which one of the following statements must also be true?
I. x = 0
II. y = 0
III. xy = 0
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only
Given: (x − y)² = x² + y²
Expand and simplify the left side to get: x² - xy + y² = x² + y²
Subtract x² from both sides: -xy + y² = y²
Subtract y² from both sides: -xy = 0
Divide both sides by -1 to get: xy = 0
So, III is true.
However, just because xy = 0, we can't say for sure
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