SOLUTION: y^3-1/8 I see that it is 1/2 or 0.5. but i don't understand how people are getting that. Will you please explain to me how 1/2 comes about?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: y^3-1/8 I see that it is 1/2 or 0.5. but i don't understand how people are getting that. Will you please explain to me how 1/2 comes about?      Log On


   

Question 572491: y^3-1/8
I see that it is 1/2 or 0.5. but i don't understand how people are getting that. Will you please explain to me how 1/2 comes about?
Answer by KMST(5399) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that you mean that
y%5E3-1%2F8 has a zero at 1/2 and that 1/2=0.5
The equations y%5E3-1%2F8=0, y%5E3-1%2F8%2B1%2F8=0%2B1%2F8 and y%5E3=1%2F8 are equivalent.
The only solution is y=1%2F2, because
%281%2F2%29%5E3=%281%2F2%29%281%2F2%29%281%2F2%29=%281%2A1%2A1%29%2F%282%2A2%2A2%29=1%2F8
and the only real number that cubed equals 1%2F8 is 1%2F2.
From another angle:
In polynomials, one of the special products is difference of cubes. The book may say
a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
Applied to y%5E3-1%2F8=y%5E3-%281%2F2%29%5E3,