(a+b+c)²=a²+b²+c²
Proved that 1/a+1/b+1/c=0
(a+b+c)2 = a2+2*a*b+2*a*c+b2+2*b*c+c2
so we have
a2+2*a*b+2*a*c+b2+2*b*c+c2 = a2+b2+c2
Subtract a2+b2+c2 from both sides
2*a*b+2*a*c+2*b*c = 0
Divide all terms by 2*a*b*c and we are left with
1/c + 1/b + 1/a = 0
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