Question

ho minh nha

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}vàxy+yz+zx=31\)

Answer 1

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\Rightarrow x=2k;y=3k;z=5k\)

\(xy+yz+zx=6k^2+15k^2+10k^2\)

\(\Rightarrow31k^2=31\Rightarrow k^2=1\)\(\Rightarrow k=1\Rightarrow x=2;y=3;z=5\)

Answer 2

Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\Rightarrow x=2k;y=3k;z=5k\)

\(\Rightarrow xy+yz+xz=31\)

\(\Rightarrow6k^2+15k^2+10k^2=31\)

\(\Rightarrow31k^2=31\)

\(\Rightarrow k=\hept{\begin{cases}-1\\1\end{cases}}\)

Với k = 1 => x = 2;y=3;z=5

Với k = -1=> x=-2;y=-3;z=-5