Question

tìm các số x,y,z biết:

\(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\)va x + y - z = 50

Answer 1

\(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\) (1)

Áp dụng dãy tỉ số bằng nhau , ta có:

\(\left(1\right)\Leftrightarrow\dfrac{\left(x-1\right)+\left(y-2\right)-\left(z-3\right)}{2+3-4}\)

\(=\dfrac{x-1+y-2-x+3}{1}\)

\(=x+y-z=50\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=50.2=100\\y-2=50.3=150\\z-3=50.4=200\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=101\\y=152\\z=203\end{matrix}\right.\)