Sửa:
\(2021=\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{a+c}\)
\(\Leftrightarrow 2021=\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{a+c}\)
\(\Leftrightarrow 2021=\dfrac{a^2+b^2-b^2}{a+b}+\dfrac{b^2+c^2-c^2}{b+c}+\dfrac{c^2+a^2-a^2}{a+c}\)
\(\Leftrightarrow 2021=\dfrac{a^2-b^2}{a+b}+\dfrac{b^2}{a+b}+\dfrac{b^2-c^2}{b+c}+\dfrac{c^2}{b+c}+\dfrac{c^2-a^2}{a+c}+\dfrac{a^2}{a+c}\)
\(\Leftrightarrow 2021=\dfrac{a^2-b^2}{a+b}+\dfrac{b^2-c^2}{b+c}+\dfrac{c^2-a^2}{a+c}+(\dfrac{b^2}{a+b}+\dfrac{c^2}{b+c}+\dfrac{a^2}{a+c})\)
\(\Leftrightarrow 2021=\dfrac{(a-b)(a+b)}{a+b}+\dfrac{(b-c)(b+c)}{b+c}+\dfrac{(c-a)(c+a)}{a+c}+M\)
\(\Rightarrow 2021=a-b+b-c+c-a+M\)
\(\Rightarrow M=2021\)
