TA CÓ:
\(a^2+b^2+c^2=ab+bc+ca\)
\(\Rightarrow2\left(a^2+b^2+c^2\right)=2\left(ab+bc+ca\right)\)
\(\Leftrightarrow2a^2+2b^2+2c^2=2ab+2bc+2ca\)
\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2bd-2ca=0\)
\(\Leftrightarrow a^2+a^2+b^2+b^2+c^2+c^2-2ab-2bc-2ca=0\)
\(\Leftrightarrow\left(a^a-2ab+b^2\right)+\left(b^2-2bc+b^2\right)+\left(a^2-2ca+c^2\right)=0\)
\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=0\)
\(\Rightarrow a=b=c\left(đpcm\right)\)
a2 + b2 + c2 = ab + bc + ca => 2(a2 + b2 + c2) = 2(ab + bc + ca)
=> 2a2 + 2b2 + 2c2 = 2ab + 2bc + 2ca
=> 2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0
=> (a2 - 2ab + b2) + (b2 - 2bc + c2) - (c2 - 2ca + a2) = 0
=> (a - b)2 + (b - c)2 + (c - a)2 = 0
=> (a - b)2 = 0 ; (b - c)2 = 0 ; (c - a)2 = 0 => a - b = 0 ; b - c = 0 ; c - a = 0
=> a = b = c
