SOLUTION: The equation {{{ (x^3+14)(x^3-51)=1014 }}} has two different real roots. Find the difference between those 2 roots

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Question 1188800: The equation +%28x%5E3%2B14%29%28x%5E3-51%29=1014+ has two different real roots. Find the difference between those 2 roots
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let y = x^3.


Then your equation takes the form


    (y+14)*(y-51) = 1014.


Reduce it to the standard quadratic equation form and solve it by any method.


    y^2 + 14y - 51y - 14*51 = 1014

    y^2 - 37y - 1728 = 0


The roots are 64 and -27.


Hence,  two different roots of the original equation are 4 and -3. 
 
The difference between them is  4 - (-3) = 7.       ANSWER

Solved.