Question

Answer 1

cuuws sapws noop

 

Answer 2

\(\left(a-\dfrac{4}{3}\right)^2+\left(b-\dfrac{4}{3}\right)^2+\left(c-\dfrac{4}{3}\right)^2\\ =a^2+b^2+c^2-\dfrac{8}{3}\left(a+b+c\right)+\dfrac{16}{9}\cdot3\\ =a^2+b^2+c^2-\dfrac{8}{3}\cdot2+\dfrac{16}{3}\\ =a^2+b^2+c^2-\dfrac{16}{3}+\dfrac{16}{3}=a^2+b^2+c^2\)

Lại có \(a+b+c=2\Leftrightarrow\left(a+b+c\right)^2=4\)

\(\Leftrightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=4\\ \Leftrightarrow a^2+b^2+c^2=4-2\left(ab+bc+ca\right)=2\left[2-\left(ab+bc+ca\right)\right]\\ \Leftrightarrow\dfrac{a^2+b^2+c^2}{2}=2-\left(ab+bc+ca\right)\)

Thay vào \(P\Leftrightarrow P=\dfrac{\dfrac{a^2+b^2+c^2}{2}}{a^2+b^2+c^2}=\dfrac{1}{2}\)