Question

[Nguyen Tuong Linh]

a 5x = 7y = x +2y = 51

b x/5 = y /4 và x^2 -  y^2 =1

c x/y = 2/5 và xy=40

Answer 1

[Nguyễn Lê Phước Thịnh]

a: Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{7}=\dfrac{y}{5}=\dfrac{x+2y}{7+2\cdot5}=\dfrac{51}{17}=3\)

Do đó: x=21; y=15

Answer 2

[Lấp La Lấp Lánh]

a) \(\Rightarrow\dfrac{x}{7}=\dfrac{y}{5}=\dfrac{2y}{10}=\dfrac{x+2y}{7+10}=\dfrac{51}{17}=3\)

\(\Rightarrow\left\{{}\begin{matrix}x=3.7=21\\y=3.5=15\end{matrix}\right.\)

b) \(\dfrac{x}{5}=\dfrac{y}{4}\Rightarrow\dfrac{x^2}{25}=\dfrac{y^2}{16}=\dfrac{x^2-y^2}{25-16}=\dfrac{1}{9}\)

\(\Rightarrow\left\{{}\begin{matrix}x^2=\dfrac{25}{9}\\y^2=\dfrac{16}{9}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=\dfrac{4}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x=-\dfrac{5}{3}\\y=-\dfrac{4}{3}\end{matrix}\right.\end{matrix}\right.\)

c) \(\dfrac{x}{y}=\dfrac{2}{5}\Rightarrow\dfrac{x}{2}=\dfrac{y}{5}=k\)

\(\Rightarrow\left\{{}\begin{matrix}x=2k\\y=5k\end{matrix}\right.\)

\(\Rightarrow xy=10k^2=40\Rightarrow k=\pm2\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=4\\y=10\end{matrix}\right.\\\left\{{}\begin{matrix}x=-4\\y=-10\end{matrix}\right.\end{matrix}\right.\)