Question

\(\left(a+b+c\right)^2=3\left(a^2+b^2+c^2\right)\)chứng min rằng a = b = c nếu có 1 trong các điều kiện sau

Answer 1

\(a^2+b^2+c^2+2ab+2bc+2ca=3a^2+3b^2+3c^2\)

\(2a^2+2b^2+2c^2-2ab-2bc-2ac=0\)

\(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)

\(\left\{{}\begin{matrix}a-b=0\\b-c=0\\c-a=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\Leftrightarrow a=b=c}\)

Answer 2

a² +b² +c² +2ab +2bc +2ca = 3a² +3b² +3c² .

2a² +2b² +2c² -2ab -2bc -2ac = 0.

( a - b )² + ( b - c )² + ( c - a )² = 0.