SOLUTION: if x²=x³, give the two possible values for x

Algebra ->  Exponents -> SOLUTION: if x²=x³, give the two possible values for x      Log On


   

Question 639191: if x²=x³, give the two possible values for x
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if x²=x to the power of 3, give the two possible values for x
------
x%5E2+=+x%5E3
x%5E3+-+x%5E2+=+0
x = 0, 0, 1
------
A 3rd order equation always has 3 solutions. Sometimes it's the same number more than once.
In this case, x = 0 with a multiplicity of 2, and x = 1.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
          x² = x³

Get 0 on the right

     x² - x³ = 0

Factor the left side:

    x²(1-x) = 0

Use the zero-factor property:

x² = 0; 1-x = 0
 x = 0;  -x = -1
          x = 1

We get two values for x. They are 0 and 1.

Edwin