Question

aflati valoarea raportului x/y, daca x+y/2x -3y =7/4 si x,y apartin R, y egal taiat 0, 2x egal taiat 3y

Answer 1

(x+y)/(2x -3y) =7/4
cum y 'egal taiat" 0 , iseamna ca putem imparti la y
(x/y+1)/(2x/y-3)=7/4

notam x/y =z
(z+1)/(2z-3)=7/4
produs mezi=produs extremi
7(2z-3)=4(z+1)
14z-21=4z+4
10z=25
z=2,5=5/2

x/y=5/2

verificare:
x=2,5 y
(2,5y+y)/(5y-3y)=3,5y/2y=3,5/2=35/20=7/4 adevarat, bine rezolvat

Answer 2

Notăm : 

[tex]\it \dfrac{x}{y} =k \ \ \ \ \ (1) \\ \\ \\ (1) \Rightarrow x = yk \ \ \ \ (2) \\ \\ \\ \dfrac{x+y}{2x-3y} = \dfrac{7}{4} \stackrel{(2)}{\Longrightarrow} \dfrac{yk+y}{2yk-3y} =\dfrac{7}{4} \Rightarrow \dfrac{y(k+1)}{y(2k-3)} = \dfrac{7}{4} \Rightarrow \dfrac{k+1}{2k-3} = \dfrac{7}{4} \Rightarrow \\ \\ \\ \Rightarrow 4k+4=14k-21 \Rightarrow 4+21= 14k-4k \Rightarrow 25=10k \Rightarrow \\ \\ \\ \Rightarrow 10k = 25|_{:10} \Rightarrow k = 2,5 \Rightarrow \dfrac{x}{y} =2,5[/tex]