Question

if 3(a²+b²+c²)=(a+b+c)² then find out the relation between a,b and c?

Answer 1

since (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
so 3a^2+3b^2+3c^2=a^2+b^2+c^2+2(ab+bc+ca)
i.e on solving is 2a^2+2b^2+2c^2=2(ab+bc+ca)
2(a^2+b^2+c^2)=2(ab+bc+ca)
so a^2+b^2+c^2=ab+bc+ca
on resolving the expression a^2+b^2+c^ we get on lhs (a+b+c)^-2(ab+bc+ca)
so (a+b+c)^2=3(ab+bc+ca)