Question

if a^2+b^2+c^2-ab-bc-ca<=0 then value a+b/c ( a,b,c not equal to 0)

Answer 1

First, multiply by two.

Can we find information from $2a^2+2b^2+2c^2-2ab-2bc-2ca$? If we have learned identity, we can know it is a sum of $(a-b)^2+(b-c)^2+(c-a)^2$.

Therefore, $(a-b)^2+(b-c)^2+(c-a)^2\geq 0$ is required. From the question, we are given $(a-b)^2+(b-c)^2+(c-a)^2\leq 0$.

∴$(a-b)^2+(b-c)^2+(c-a)^2=0$

Therefore, a=b=c is required.

So the answer to your question is 2.