SOLUTION: if x = y^2 and y = x^2, what is the least possible real value of x^2 + x + 1, where x and y are complex numbers ?

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Question 526130: if x = y^2 and y = x^2, what is the least possible real value of x^2 + x + 1,
where x and y are complex numbers ?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have

(if x is not equal to 0). Hence the three possible values of x (roots of unity) are:


, and
.

Hence, replacing each of these values into the expression x^2 + x + 1 and simplifying yields 3, 0, and 0 respectively, so the minimum value is 0.