Find: a^2/(bc) + b^2/(ca) + c^2/(ab) = ? | Olympiad Question

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If a+b+c=0 find the value ab/a²+ab+b² +bc/b²+bc+c² +ca/c²+ca+a² If a+b+c=0 find the value ab/a²+ab+b² +bc/b²+bc+c² +ca/c²+ca+a²
If ab + bc + ca = 36 and a^2+b^2+c^2=85, then find a + b + c. If ab + bc + ca = 36 and a^2+b^2+c^2=85, then find a + b + c.
Prove that - [(x^a/b^b)^(a^2+ab+b^2)] [(x^b /x^c)^(b^2+bc+c^2] [(x^c/xa) ^(c^2+ac+c^2)] = 1 Prove that - [(x^a/b^b)^(a^2+ab+b^2)] [(x^b /x^c)^(b^2+bc+c^2] [(x^c/xa) ^(c^2+ac+c^2)] = 1
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