Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{m_a}^2 = \frac{{{b^2} + {c^2}}}{2} - \frac{{{a^2}}}{4} \Rightarrow 4{m_a}^2 = 2\left( {{b^2} + {c^2}} \right) - {a^2} = 2{b^2} + {a^2} + {b^2} - {a^2} = 3{b^2}\\
\Rightarrow {m_a} = \frac{{\sqrt 3 }}{4}b\\
{m_b}^2 = \frac{{{a^2} + {c^2}}}{2} - \frac{{{b^2}}}{4} \Rightarrow 4{m_b}^2 = 2\left( {{a^2} + {c^2}} \right) - {b^2} = 2{a^2} + {a^2} + {b^2} - {b^2} = 3{a^2}\\
\Rightarrow {m_b} = \frac{{\sqrt 3 }}{2}a\\
{m_c}^2 = \frac{{{a^2} + {b^2}}}{2} - \frac{{{c^2}}}{4} = {c^2} - \frac{{{c^2}}}{4} = \frac{{3{c^2}}}{4} \Rightarrow {m_c} = \frac{{\sqrt 3 }}{2}c\\
\Rightarrow {m_a} + {m_b} + {m_c} = \frac{{\sqrt 3 }}{2}\left( {a + b + c} \right)
\end{array}\)
