Question

Tìm x; y; z thỏa:

5x=2y ; 2x=3z ; x.y = 90

giúp mk nhé

cảm ơn m.n nhìu

Answer 1

Từ \(5x=2y\)\(\Rightarrow\frac{x}{y}=\frac{2}{5}\)

Từ \(2x=3z\)\(\Rightarrow\frac{x}{z}=\frac{3}{2}\)

Từ \(xy=90\)\(\Rightarrow x=\frac{90}{y};y=\frac{90}{x}\)

Ta có: \(\frac{x}{y}=\frac{2}{5}\)

Mà \(x=\frac{90}{y}\)

Nên \(\frac{\frac{90}{y}}{y}=\frac{2}{5}\)\(\Leftrightarrow\frac{90}{y^2}=\frac{2}{5}\)\(\Leftrightarrow y=\pm15\)

*Khi \(y=15\) thì \(x=\frac{90}{15}=6\) và \(z=\frac{6.2}{3}=4\)

*Khi \(y=-15\) thì \(x=\frac{90}{-15}=-6\) và \(z=\frac{-6.2}{3}=-4\)

Vậy \(\left\{x;y;z\right\}\in\left\{\left(6;15;4\right),\left(-6;-15;-4\right)\right\}\)