A ^ 2 + B ^ 2 + C ^ 2-ab-bc-ac = 0, the size relationship of ABC ABC is all positive

a^2+b^2+c^2-ab-bc-ac=0
Both sides at the same time x2
2a^2+2b^2+2c^2-2ab-2bc-2ac=0
a^2+2ab+b^2+b^2+2bc+c^2+c^2+2ac+a^2=0
Complete square
(a-b)^2+(b-c)^2+(a-c)^2=0
Are all nonnegative numbers
Only 0 + 0 + 0 = 0
a-b=0
a=b
b-c=0
b=c
a-c=0
We get a = b = C
equal
a=c

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