Should be an easy proof but have no idea how to do it

[slow bobcat]

Prove that if a^2+ab+b^2=0, then a = 0 and b = 0. The problem is that you need to use a^3-b^3 somehow for this, instead of quadratic equation theory.

[keen frigate]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[terse surge]

$$
a^2+ab+b^2=0 \

a =0 \quad b=0
$$

Well, you know that $a^2 + 2ab +b^2 = (a+b)^2$ and only way to get that to equal to 0 is if a=-b or a=b=0, from here you should be able to show that then for this to be true

$$
0=a^2 + ab +b^2 + ab = ab$
$$

a has to equal - b or a=b=0, but $a = -b = 0 \text{ iff } a=b=0$ so therefore $a=b=0$

[golden moss]

conquestace
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[slow bobcat]

Thanks!

+close