good equation o solve

i am excited to see the solution:

(a-b)(b-c)(c-a)=a^{2}+b^{2}+c^{2}

3 Answers

341
Hari Shankar ·

i think latex is playing truant again. could u type it out using the editor?

341
Hari Shankar ·

If a,b,c are real, LHS≤0 and RHS≥0, so only solution is (0,0,0)

11
Mani Pal Singh ·

If a,b,c are real, LHS≤0 and RHS≥0, so only solution is (0,0,0)

How LHS≤0?

take 1,2,3
we get lhs≥0

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