Question

[Nguyễn Huyền Anh]

cho1/a+1/b+1/c=0 chứng minh (a+b+c)^2=a^2+b^2+c^2

Answer 1

[Pham Van Hung]

\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\Rightarrow\frac{ab+bc+ac}{abc}=0\Rightarrow ab+bc+ac=0\)

\(\Rightarrow2ab+2bc+2ac=0\Rightarrow a^2+b^2+c^2+2ab+2bc+2ac=a^2+b^2+c^2\)

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