[GMAT math practice question]
x^3-y^3 = 9 and x-y = 3. What is the value of xy?
A. -2
B. -1
C. 0
D. 1
E. 2
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x^3-y^3 = 9 and x-y = 3. What is the value of xy?
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Max@Math Revolution
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x^3-y^3 = (x-y)(x^2+xy+y^2) = 3(x^2+xy+y^2) = 9
Therefore, x^2+xy+y^2 = 3.
Now,
x^2+xy+y^2 = (x-y)^2 + 3xy = 3^2 + 3xy = 9 + 3xy = 3.
So,
3xy = -6
and xy = -2.
Therefore, the answer is A.
Answer: A
x^3-y^3 = (x-y)(x^2+xy+y^2) = 3(x^2+xy+y^2) = 9
Therefore, x^2+xy+y^2 = 3.
Now,
x^2+xy+y^2 = (x-y)^2 + 3xy = 3^2 + 3xy = 9 + 3xy = 3.
So,
3xy = -6
and xy = -2.
Therefore, the answer is A.
Answer: A
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