Question

\(\frac{x}{2}\)=\(\frac{y}{3}\) và x*y=52

Answer 1

Đặt \(\frac{x}{2}=\frac{y}{3}=k\Rightarrow\hept{\begin{cases}x=2k\\y=3k\end{cases}}\)

Khi đó x.y = 52

<=> 2k.3k = 52

=> 6k² = 52

=> k² = 52/6

=> k = \(\pm\sqrt{\frac{52}{6}}\)

Khi k = \(\sqrt{\frac{52}{6}}\Rightarrow\hept{\begin{cases}x=\sqrt{\frac{52}{6}}.2=\sqrt{\frac{104}{3}}\\y=\sqrt{\frac{52}{6}}.3=\sqrt{78}\end{cases}}\)

Khi k = \(-\sqrt{\frac{52}{6}}\Rightarrow\hept{\begin{cases}x=-\sqrt{\frac{52}{6}}.2=-\sqrt{\frac{104}{3}}\\x=-\sqrt{\frac{52}{6}}.3=-\sqrt{78}\end{cases}}\)

Answer 2

Đặt : \(\hept{\begin{cases}x=2k\\y=3k\end{cases}}\)

Ta có : \(xy=52\Leftrightarrow2k.3k=52\)

\(\Leftrightarrow6k^2=52\Leftrightarrow k^2=\frac{26}{3}\Leftrightarrow k=\pm\sqrt{\frac{26}{3}}\)

TH1 : k = \(\sqrt{\frac{26}{3}}\)

\(x=2.\sqrt{\frac{26}{3}}=\frac{2\sqrt{78}}{3}\); \(y=3.\sqrt{\frac{26}{3}}=\sqrt{78}\)

TH2 : k = \(-\sqrt{\frac{26}{3}}\)

\(x=2.\left(-\sqrt{\frac{26}{3}}\right)=-\frac{2\sqrt{78}}{3}\); \(y=3.\left(-\sqrt{\frac{26}{3}}\right)=-\sqrt{78}\)