Bunuel wrote:
If \(x^2 + y^2 = xy\), then \((x + y)^4 =\)
(A) \(xy\)
(B) \(x^2*y^2\)
(C) \(9x^2*y^2\)
(D) \((x^2 + y^2)^2\)
(E) \(x^4 + y^4\)
We are given:
x^2 + y^2 = xy.
Note that (x + y)^4 = [(x + y)^2]^2 = [x^2 + 2xy + y^2]^2.
Since x^2 + y^2 = xy,
[x^2 + 2xy + y^2]^2 = [2xy + xy]^2 = (3xy)^2 = 9(x^2)(y^2).
Answer: C
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