SOLUTION: How many real numbers are there such that the 5th power of the number is the sum of the 4th and 3rd powers of the number? a) 1 b) 2 c) 3 d) 5 e) none of these

Question 283083: How many real numbers are there such that the 5th power of the number is the sum of the 4th and 3rd powers of the number?
a) 1 b) 2 c) 3 d) 5 e) none of these

Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
So, we want:

In other words we are asking when
?
In even more words we are asking when
?
We note that x=0 certainly makes the statement true. Now, will give two real (irrational) roots. So, strictly speaking there are three real numbers that meet the criterion: {0, 1/2 (1 - Sqrt[5]), 1/2 (1 + Sqrt[5]).
However, one should note that x=0 occurs as a root three times.
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