# Hoping someone can help for once! a^3 = b^3

• Feb 9th 2009, 02:39 PM
glover_m
Hoping someone can help for once! a^3 = b^3
Show that if a^3 = b^3 if and only if a=b

Suppose a = b

a^3 = (a)(a)(a)
=(b)(b)(b)
=b^3

Prove other direction using contrapositive:

Suppose a != b, then a^3 != b^3

Case 1:
a>b

****I'm a little stuck here, I'm not sure if I'm allowed to say aaa>bbb by assuming a>b

a^3 = (a)(a)(a)
>(b)(b)(b)
=b^3

a^3 != b^3
• Feb 9th 2009, 02:57 PM
Plato
Quote:

Originally Posted by glover_m
Show that if a^3 = b^3 if and only if a=b

Suppose that $\displaystyle p \ne q\;\& \,p^3 = q^3$, that means $\displaystyle 0 = p^3 - q^3 = \left( {p - q} \right)\left( {p^2 + qp + q^2 } \right)$.
But because $\displaystyle p \ne q$ this means that it must be $\displaystyle \left( {p^2 + qp + q^2 } \right)=0$.
Use the classic quadratic formula to prove $\displaystyle p$ has no real roots.
• Feb 9th 2009, 03:00 PM
glover_m
clutch thnx brah
• Feb 9th 2009, 03:10 PM
Plato
Quote:

Originally Posted by glover_m
clutch thnx brah

What in the world do those nonsense symbol-strings mean?
Please use standard English on this forum.