Question

Daca $2 x^{2} -5xy+3 y^{2} =0$ atunci $\frac{x}{y}$ ∈ {...}

Answer 1

$2x^2-5xy+3y^2=0 \\ \\ 2x^2-2xy-3xy+3y^2-0 \\ \\ 2x(x-y)-3y(x-y)=0 \\ \\ (x-y)(2x-3y)=0 \Rightarrow x=y~sau~2x=3y. \\ \\ x=y \Rightarrow \frac{x}{y} =1. \\ \\ 2x=3y \Rightarrow \frac{x}{y} = \frac{3}{2}. \\ \\ Deci~ \frac{x}{y} \in \Big\{1;~ \frac{3}{2} \Big\} . \\ \\ Observatie:~x,y \neq 0.$