SOLUTION: if 3√x^6 + 3√8x^3 + 3 √1=0, then x = A -1 B 0 C 1 D 2 E 3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: if 3√x^6 + 3√8x^3 + 3 √1=0, then x = A -1 B 0 C 1 D 2 E 3      Log On


   

Question 104640: if 3√x^6 + 3√8x^3 + 3 √1=0, then x =
A -1
B 0
C 1
D 2
E 3
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%28x%5E6%29%2B3sqrt%288x%5E3%29%2B3sqrt%281%29=0
sqrt%28x%5E6%29%2Bsqrt%288x%5E3%29%2Bsqrt%281%29=0
x%5E3%2B2x%2Asqrt%28x%29%2B1=0
x%5E3%2B1=-2x%2Asqrt%28x%29
%28x%5E3%2B1%29%5E2=%28-2x%2Asqrt%28x%29%29%5E2
x%5E6%2B2x%5E3%2B1=8x%5E3
x%5E6%2B2x%5E3%2B1-8x%5E3=8x%5E3-8x%5E3
x%5E6-6x%5E3%2B1=0
Let___y=x%5E3
____y%5E2=x%5E6
Then,
x%5E6-6x%5E3%2B1=y%5E2-6y%2B1
y%5E2-6y%2B1=0
y=%286%2B-sqrt%286%5E2-4%2A1%2A1%29%29%2F%282%2A1%29
y=%286%2B-sqrt%2836-4%29%29%2F%282%29
y=6%2B-sqrt%2832%29%29%2F%282%29
y=6%2B-+4sqrt%282%29%29%2F%282%29
y=3%2B2sqrt%282%29 or y=y=3-2sqrt%282%29
Then,
x=%283%2B2sqrt%282%29%29%5E3 or x=%283-2sqrt%282%29%29%5E3