If $a, b, c$ are real numbers such that $(a-2)^{2}+(b-2)^{2} +(c-2)^{2}=0$\

Question

Professor PC Thomas Classes · Answer

(a) : Since, the sum of squares equals to 0 , so each term must be 0 .\ $\Rightarrow \quad a-2=0, b-2=0$ and $c-2=0$\ $\Rightarrow \quad a=b=c=2$\ $	herefore \quad a, b, c$ are in G.P. with common ratio 1\ Also, $a+b+c=2+2+2=6$\