SOLUTION: The equation {{{ (x^3+73)(x^3-164)=15028 }}} had two different real roots. Find the difference between these two roots.

Algebra ->  Expressions -> SOLUTION: The equation {{{ (x^3+73)(x^3-164)=15028 }}} had two different real roots. Find the difference between these two roots.      Log On


   

Question 1105034: The equation +%28x%5E3%2B73%29%28x%5E3-164%29=15028+ had two different real roots. Find the difference between these two roots.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is also x^6-91x^3-11972=15028
or x^6-91x^3-27000=0
The discriminant is sqrt(116281)=341.
x^3=(1/2)(91+/-341)=216, so x=6
and x^3=-125, so x=-5
The difference between 6 and -5 is 11.
graph%28300%2C300%2C-10%2C10%2C-5000%2C5000%2C%28x%5E3%2B73%29%28x%5E3-164%29-15028%29