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Homework Statement
Let x and y be real numbers with x+y=1 and (x2 + y2)(x3 + y3) = 12. What is the value of x2 + y2 ?
Homework Equations
Sum of Cubes: (a3 + b3) = (a+b)(a2-ab+b2)
The Attempt at a Solution
I plugged in the sum of cubes to the equation that equals 12 to get:
(x2 + y2)(x+y)(x2-xy+y2) = 12
and since (x+y) = 1,
(x2 + y2)(x2-xy+y2) = 12
and therefore,
(x2 + y2)(x2-xy+y2) = (x2 + y2)(x3 + y3)
cancellation:
(x+y)(x2-xy+y2) = (x3 + y3) = 12
then I plugged (x3 + y3) for 12 to the original equation:
(x2 + y2)(x3 + y3) = (x3 + y3)
and that means that (x2 + y2) = 1, right?