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If x plus y equals -2 and xy equals 2 then what is x cubed plus y cubed?
Wiki User
∙ 14y ago
x + y = -2
∴ y = -2 - x
xy = 2
∴ x(-2 - x) = 2
∴ -2x - x2 = 2
∴ x2 + 2x + 2 = 0
∴ x2 + 2x + 1 = -1
∴ (x + 1)2 = -1
∴ x + 1 = i
∴ x = i - 1
recall: y = - 2 - x
∴ y = - 2 - (i - 1)
∴ y = -2 - i + 1
∴ y = - i - 1
∴ x3 + y3 = (i - 1)3 + (- i - 1)3
= (i - 1)(i2 - 2i + 1) + (- i - 1)(i2 + 2i + 2)
= i3 - 2i2 + i - i2 + 2i - 1 - i3 - 2i2 - 2i - i2 - 2i - 2
= i3 - i3 - 2i2 - i2 - 2i2 - i2 + i + 2i - 2i - 2i - 1 - 2
= -6i2 - i - 3
= 3 - i
Wiki User
∙ 14y ago
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