Giải thích các bước giải:
Ta có :
$x+y+z=\sqrt{3a}$
$\rightarrow (x+y+z)^2=3a$
$\rightarrow x^2+y^2+z^2+2(xy+yz+zx)=3a$
$\rightarrow a+2(xy+yz+zx)=3a$
$\rightarrow xy+yz+zx=a$
$\rightarrow a+x^2=xy+yz+zx+x^2=(x+y)(x+z)$
Tương tự $a+y^2=(y+x)(y+z),a+z^2=(z+x)(z+y)$
$\rightarrow$Biểu thức ban đầu
$P=x.\sqrt{\dfrac{(y+z)(y+x).(z+x)(z+y)}{(x+y)(x+z)}}+y.\sqrt{\dfrac{(x+z)(x+y).(z+x)(z+y)}{(y+z)(y+z)}}+z.\sqrt{\dfrac{(y+z)(y+x).(x+z)(x+y)}{(z+y)(z+x)}}$
$\rightarrow P=x(y+z)+y(x+z)+z(x+y)=2(xy+yz+zx)=2a$
