Question

[lê huỳnh nhân]

tìm x,y,z:x/5=y/7=z/3và x^2+y^2+z^2=585

Answer 1

[Nguyễn Lê Phước Thịnh]

Đặt \(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{3}=k\)

=>x=5k; y=7k; z=3k

\(x^2+y^2+z^2=585\)

\(\Leftrightarrow25k^2+49k^2+9k^2=585\)

\(\Leftrightarrow k^2=\dfrac{585}{83}\)

Trường hợp 1: \(k=\sqrt{\dfrac{585}{83}}\)

\(\Leftrightarrow x=5\sqrt{\dfrac{585}{83}};y=7\sqrt{\dfrac{585}{83}};z=3\sqrt{\dfrac{585}{83}}\)

Trường hợp 2: \(k=-\sqrt{\dfrac{585}{83}}\)

\(\Leftrightarrow x=-5\sqrt{\dfrac{585}{83}};y=-7\sqrt{\dfrac{585}{83}};z=-3\sqrt{\dfrac{585}{83}}\)