Question

cho \(\dfrac{x}{2}=\dfrac{y}{5}\) biết x*y=90.tính x,y

Answer 1

Đặt \(\dfrac{x}{2}=\dfrac{y}{5}=k\)

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

Mà \(xy=90\)

\(\Rightarrow2k.5k=90\)

\(\Rightarrow10k^2=90\)

\(\Rightarrow k^2=\dfrac{90}{10}\)

\(\Rightarrow k^2=9\)

\(\Rightarrow k=\sqrt{9}=3=-3\)

Xét trường hợp 1: \(k=3\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.3=6\\y=5.3=15\end{matrix}\right.\)

Xét trường hợp 2: \(k=-3\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-3\right)=-6\\y=5.\left(-3\right)=-15\end{matrix}\right.\)

Vậy x=6 thì y=15 hoặc x=-6 thì y=-15

Answer 2

Đặt \(\dfrac{x}{2}=\dfrac{y}{5}=a\)
=> x = 2a ; y = 5a
Ta có x . y = 90
<=> 2a . 5a = 90
<=> 10a² = 90
<=> a² = 90 : 10
<=> a² = 9
<=> a = 3
Suy ra: x = 2 . 3 = 6
y = 5 . 3 = 15