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solve for x:(x-4)^3 =(1/8)^(-1)

 Jul 30, 2023
 #1
avatar+115 
0

When we open 1 side of the equation  (x-4)^3 we get :

 

x^3 - 12x^2 + 48x - 64 =8

 

Now we simply 

 

x^3 - 12x^2 + 48x = 72 

 

Now we move everything to 1 side to isolate then set = 0 , then factor 

 

thus x=6 smiley

 Jul 30, 2023
 #2
avatar+183 
-2

If we are only looking for real answers, we could directly take the cube root and see that \(x=6\) is a solution. However, if we also want complex solutions we would proceed as @breadstick presented, and since we know \(x-6\) is a factor we could divide and use the quadratic formula from there.

 Aug 1, 2023

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