Question

x phan 2 = y phan 5 va xy = 90

trinh bay ra nha

Answer 1

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

Ta có : \(\left(\frac{x}{2}\right)^2=\frac{x}{2}\cdot\frac{x}{2}=\frac{x}{2}\cdot\frac{y}{5}=\frac{xy}{10}=\frac{90}{10}=9\)

Từ đây suy ra \(\left(\frac{x}{2}\right)^2=9\)

\(\Rightarrow\frac{x}{2}=\left\{\pm3\right\}\)

TH1: \(\frac{x}{2}=\frac{y}{5}=3\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=3\\\frac{y}{5}=3\end{cases}\Rightarrow\hept{\begin{cases}x=6\\y=15\end{cases}}}\)

TH2: \(\frac{x}{2}=\frac{y}{5}=-3\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=-3\\\frac{y}{5}=-3\end{cases}}\Rightarrow\hept{\begin{cases}x=-6\\y=-15\end{cases}}\)

Vậy....

Answer 2

Đề bài: \(\frac{x}{2}\)= \(\frac{y}{5}\) và xy = 90

Ta có: \(\frac{x}{2}\)= \(\frac{y}{5}\)= k ( k thuộc Q )

\(\hept{\begin{cases}x=2k\\y=5k\end{cases}}\) 

Mà xy = 90

<=> 2k.5k = 90

<=> 10k\(^2\) = 90

<=> k\(^2\)= 90 : 10

<=> k\(^2\)= 9

<=>\(\hept{\begin{cases}k=3\\k=\left(-3\right)\end{cases}}\)

Answer 3

Đặt : \(\frac{x}{2}=\frac{y}{5}=k\)

\(\Rightarrow x=2k;y=5k\)

\(\Rightarrow2k.5k=90\)

\(\Rightarrow7k=90\)

\(\Rightarrow k=\frac{90}{7}\)

........

Answer 4

Đặt \(\frac{x}{2}=\frac{y}{5}=k\left(k\ne0\right)\)

\(\Rightarrow x=2k\); \(y=5k\)

\(\Rightarrow xy=2k.5k=10k^2=90\)

\(\Rightarrow k^2=9\)\(\Rightarrow k=\pm3\)

Nếu \(k=-3\)\(\Rightarrow x=-3.2=-6\); \(y=-3.5=-15\)

Nếu \(k=3\)\(\Rightarrow x=3.2=6\); \(y=3.5=15\)

Vậy các cặp giá trị \(\left(x;y\right)\)thoả mãn là \(\left(-6;-15\right)\), \(\left(6;15\right)\)