Question

cho a2 + b2 + c2 -ab + bc + ca=0 chứng minh rằng a = b = c

Answer 1

sửa đề :a2 +b2 +c2 -( ab +bc +ac ) =0

=> 2a2+2b2+2c2 - 2ab-2bc-2ac =0

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

=>\(\left[{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\) =>a=b=c.

Answer 2

Sửa đề :a2 +b2 +c2 -( ab +bc +ac ) =0

=> 2a2+2b2+2c2 - 2ab-2bc-2ac =0

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

\(\Rightarrow\left[{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\Rightarrow a=b=c\)