SOLUTION: (x-4)^4= 81

Algebra ->  Equations -> SOLUTION: (x-4)^4= 81      Log On


   

Question 397630: (x-4)^4= 81
Found 2 solutions by robertb, richard1234:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-4%29%5E4=+81
==> %28x-4%29%5E4+-+81=0
<==> %28%28x-4%29%5E2+-+9%29%28%28x-4%29%5E2+%2B+9%29+=+0
<==> (x- 4-3)(x - 4 +3)(x -4 - 3i)(x - 4 + 3i) = 0
<==> (x -7)(x -1)(x -4 - 3i)(x - 4 + 3i) = 0
Then the solutions to the original equation are (including imaginary roots) are
7,1, 4 + 3i, 4 - 3i.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
81 has four roots of unity: 3, 3i, -3, -3i.

We have the equations

x-4 = 3
x-4 = 3i
x-4 = -3
x-4 = -3i

all of which can easily be solved for x.