SOLUTION: I can't understand how the solution set to (x-4)^(2/3)=16 is {-60,68}? I need precise step-by-step info, because I am looking at an example problem, and I'm still not getting it.
Question 876668: I can't understand how the solution set to (x-4)^(2/3)=16 is {-60,68}? I need precise step-by-step info, because I am looking at an example problem, and I'm still not getting it. Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website! (x-4)^(2/3)=16
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Take the sq root of both sides
(x-4)^(1/3)= 4
Cube both sides
x-4 = 64
x = 68
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Do the same with sqrt(16) = -4
Here's an alternate way. Slightly different:
We want to make the exponent become a whole
number. So we raise both sides to the 3 power. That is,
we cube both sides:
Use the principle of square roots:
x-4 = 64; x-4 = -64
x = 68; x = -68
Edwin