SOLUTION: If x² + x = 1, Then find (x^5 + 8)/(x + 1)

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Question 1145439: If x² + x = 1, Then find (x^5 + 8)/(x + 1)
Answer by thmei1(4) About Me  (Show Source):
You can put this solution on YOUR website!
x² + x = 1 , is the same as x² + x - 1 = 0, it is a quadratic so you can solve for x using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 1, b = 1, c = -1
which will end up being
x = - (1 +- sqrt(5)) / 2
+- results in two answers
substitute - (1 + sqrt(5)) / 2 into x in the problem (x^5 + 8) / (x + 1) = 5
substitute - (1 - sqrt(5)) / 2 into x in the problem (x^5 + 8) / (x + 1) = 5
in this case if you plug in the two different x given by the quadratic formula you only end up with x = 5
Answer : x = 5