Question

CMR: a= b= c . Nếu,

a, 2( a² + b² + c² ) = ab + bc + ca

b,2 ( a² + b² + c² ) - 2( ab + bc + ca ) = 0

c, ( a + b + c )² = 3( ab + bc + ca )

Answer 1

b: \(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2bc-2ac=0\)

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

=>(a-c)^2+(a-b)^2+(b-c)^2=0

=>a=b=c

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

\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2bc-2ac=0\)

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

=>(a-b)^2+(a-c)^2+(b-c)^2=0

=>a=b=c