SOLUTION: (x to the power of 3)-(9x to the power of 3/2)+8=0--- How would you solve this for x?

Question 1017021: (x to the power of 3)-(9x to the power of 3/2)+8=0--- How would you solve this for x?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^3-9x^(3/2)+8=0
(x^3/2-8)(x^3/2-1)=0. You can potentially factor if the first term is twice the power of the second, and the last is constant. Usually, it is x^4+x^2+c=0, but this works.
These are differences of cubes, the cube of x^(1/2)
(x^1/2-2)(x+2x^(1/2)+4)=0 and (x^1/2-1)(x+x^(1/2)+1)=0
sqrt(x)=2, x=4
sqrt(x)=1, x=1

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