Đáp án:
\(P = \frac{1}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
a + b + c = 2\\
\Rightarrow {(a + b + c)^2} = 4\\
\Leftrightarrow {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ca = 4\\
\Leftrightarrow ab + bc + ca = \frac{{4 - ({a^2} + {b^2} + {c^2})}}{2}\\
P = \frac{{2 - (ab + bc + ca)}}{{{{(a - \frac{4}{3})}^2} + {{(b - \frac{4}{3})}^2} + {{(c - \frac{4}{3})}^2}}}\\
= \frac{{2 - \frac{{4 - ({a^2} + {b^2} + {c^2})}}{2}}}{{{a^2} + {b^2} + {c^2} - \frac{8}{3}(a + b + c) + \frac{{16}}{3}}}\\
= \frac{{\frac{{{a^2} + {b^2} + {c^2}}}{2}}}{{{a^2} + {b^2} + {c^2}}} = \frac{1}{2}
\end{array}\)
