Đặt ` x/3 = k ` và ` y/4 = k `
` => ` \(\left[ \begin{array}{l}x=3k\\y=4k\end{array} \right.\)
Theo đề bài, ta có:
` y × x = 16 `
` => 4k × 3k = 16 `
` => 12k^2 = 16 `
` => k^2 = 4/3 `
` => k = ± \sqrt{\frac{4}{3}} `
* Với ` k = + \sqrt{\frac{4}{3}} ` ta có:
\(\left[ \begin{array}{l}\frac{x}{3}=+\sqrt{\frac{4}{3}}⇔x=\frac{\sqrt{4}.3}{\sqrt{3}}\\\frac{y}{4}=+\sqrt{\frac{4}{3}}⇔y=\frac{\sqrt{4}.4}{\sqrt{3}}\end{array} \right.\)
* Với ` k = - \sqrt{\frac{4}{3}} ` ta có:
\(\left[ \begin{array}{l}\frac{x}{3}=-\sqrt{\frac{4}{3}}⇔x=-\frac{\sqrt{4}.3}{\sqrt{3}}\\\frac{y}{4}=-\sqrt{\frac{4}{3}}⇔y=-\frac{\sqrt{4}.4}{\sqrt{3}}\end{array} \right.\)
