Question

1.Cho: a²+b²+c²+3=2(a+b+c) Chứng minh a=b=c

2.Cho (a+b+c)²=3(a+b+c) chứng minh a=b=c

Answer 1

1/ \(a^2+b^2+c^2+3=2\left(a+b+c\right)\Leftrightarrow\left(a^2-2a+1\right)+\left(b^2-2b+1\right)+\left(c^2-2c+1\right)=0\)

\(\Leftrightarrow\left(a-1\right)^2+\left(b-1\right)^2+\left(c-1\right)^2=0\Leftrightarrow a=b=c=1\)

2/ \(\left(a+b+c\right)^2=3\left(a+b+c\right)\Leftrightarrow\left(a+b+c\right)\left(a+b+c-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}a+b+c=0\\a+b+c=3\end{cases}}\)

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