We have:\(x:y:z=a:b:c\Leftrightarrow\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}=\dfrac{x+y+z}{a+b+c}\)

\(\Rightarrow\dfrac{x^2}{a^2}=\dfrac{y^2}{b^2}=\dfrac{z^2}{c^2}=\dfrac{\left(x+y+z\right)^2}{\left(a+b+c\right)^2}=\dfrac{x^2+y^2+z^2}{a^2+b^2+c^2}\)\(\Rightarrow\dfrac{\left(x+y+z\right)^2}{x^2+y^2+z^2}=\dfrac{\left(a+b+c\right)^2}{a^2+b^2+c^2}=\dfrac{1^2}{1}=1\)

\(\Rightarrowđpcm\)