Isolate the cube root:
Raise both sides to the 3rd power (that is, "cube" both sides)
Raising a radical to the same exponent as its index amounts
to removing the radical and the exponent, so we have:
But we must multiply the right side out:
Get 0 on one side:
We like the 0 to be on the right, so we switch sides:
Factor out of the first two terms on the left:
Factor out of the last two terms on the left:
Factor out of both terms on the left:
Factor the second parentheses as the difference of sqwuares:
Use the zero-factor principle and set each factor = 0:
x-3=0 gives solution x=3
x-1=0 gives solution x=1
x+1=0 gives solution x=-1
The solutions are -1, 1, and 3. They all check in the original.
(You only need to check radical equations for extraneous solutions
when there is a root with an even index or a denominator containg
a variable.)
Edwin
