Question

Với a, b, c không có số nào đối nhau

cmr\(\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}=\frac{b^2}{a+b}+\frac{c^2}{b+c}+\frac{a^2}{c+a}\)

Answer 1

\(\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}=\frac{b^2}{a+b}+\frac{c^2}{b+c}+\frac{a^2}{a+c}\)

\(\Leftrightarrow\frac{a^2-b^2}{a+b}+\frac{b^2-c^2}{b+c}+\frac{c^2-a^2}{a+c}=0\)

\(\Leftrightarrow\frac{\left(a+b\right)\left(a-b\right)}{a+b}+\frac{\left(b-c\right)\left(b+c\right)}{b+c}+\frac{\left(c-a\right)\left(c+a\right)}{a+c}=0\)

\(\Leftrightarrow a-b+b-c+c-a=0\)

\(\Leftrightarrow0=0\)( luôn đúng )
\(\Rightarrow\)\(\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}=\frac{b^2}{a+b}+\frac{c^2}{b+c}+\frac{a^2}{a+c}\)