SOLUTION: Solve (x^2+2x)^(1/3)=2

Algebra ->  Equations -> SOLUTION: Solve (x^2+2x)^(1/3)=2      Log On


   

Question 975106: Solve (x^2+2x)^(1/3)=2
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2B2x%29%5E%281%2F3%29=2
root%283%2C%28x%5E2%2B2x%29%29=2
%28root%283%2C%28x%5E2%2B2x%29%29%29%5E3=2%5E3
x%5E2%2B2x=8
x%5E2%2B2x-8=0
x%5E2%2B4x-2x-8+=+0
%28x%5E2%2B4x%29-%282x%2B8%29+=+0
x%28x%2B4%29-2%28x%2B4%29+=+0
%28x-2%29%28x%2B4%29+=+0

solutions:
if %28x-2%29+=+0=>highlight%28x=2%29
if %28x%2B4%29+=+0=> highlight%28x=-4%29


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve (x^2+2x)^(1/3)=2
%28x%5E2+%2B+2x%29%5E%281%2F3%29+=+2

highlight%28highlight%28%28x%5E2+%2B+2x%29%5E%28%281%2F3%29+%2A+3%29+=+2%5E3%29%29 ------- Raising both sides to the 3rd power

x%5E2+%2B+2x+=+8

x%5E2+%2B+2x+-+8+=+0

(x + 4)(x - 2) = 0

highlight_green%28system%28x+=+-+4_or%2Cx+=+2%29%29