SOLUTION: a problem on a take home test cube root of 125-xcubed =5-x do i first cube both sides to get rid of the radical or should i solve the radical on the left side if i cube both sides

Question 91636: a problem on a take home test cube root of 125-xcubed =5-x do i first cube both sides to get rid of the radical or should i solve the radical on the left side if i cube both sides i get 125- 5x to the 3 power. if take the cube root of the left side i get 5ixsquare root of 5 =5-x ihave no idea what to do please help thank you very much!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a problem on a take home test cube root of 125-xcubed =5-x do i first cube both sides to get rid of the radical or should i solve the radical on the left side if i cube both sides i get 125- 5x to the 3 power. if take the cube root of the left side i get 5ixsquare root of 5 =5-x
:
CubeRt(125 - x^3) = 5 - x
:
You can cube both sides and get rid of the radical:
Cubing right side: (5-x)^3 = (125 - 10x + x^2)*(x-5)= (125 - 75x + 15x^2 - x^3)
so you have:
125 - x^3 = 125 - 75x + 15x^2 - x^3
:
Notice you have 125 and -x^3 on both sides so get rid of those and you have:
15x^2 - 75x = 0
:
Factor out 15x
15x(x - 5) = 0
:
x = 0
and
x = +5
:
both will work in the original equation
:
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