Question

Tìm x, y biết :

\(\frac{x}{3}=\frac{y}{7};xy=84\)

Answer 1

Đặt \(k=\frac{x}{3}=\frac{y}{7}\)

Suy ra : \(k^2=\frac{x}{3}.\frac{y}{7}=\frac{xy}{21}=\frac{84}{21}=4\)

=> k = -2;2

+ k = -2 thì \(\frac{x}{3}=-2\Rightarrow x=-6\)

                  \(\frac{x}{7}=-2\Rightarrow x=-14\)

+ k = 2 thì : \(\frac{x}{3}=2\Rightarrow x=6\)

                    \(\frac{x}{7}=2\Rightarrow x=14\)

Vậy .............................

Answer 2

Đặt \(\frac{x}{3}=\frac{y}{7}=k\Rightarrow x=3k;y=7k\)

\(x.y=84\Rightarrow3k.7k=84\Rightarrow21k^2=84\Rightarrow k^2=4\Rightarrow\orbr{\begin{cases}k=2\\k=-2\end{cases}}\)

Với \(k=2\Rightarrow x=3.2=6;y=7.2=14\)

Với \(k=-2\Rightarrow x=3.\left(-2\right)=-6;y=7.\left(-2\right)=-14\)

Vậy ....