Question

determinati x,y daca 2x la patrat +25 y la patrat + 5(2x+5)-10xy=0
Ajutati.ma

Answer 1

[tex]2x^2+25y^2+5(2x+5)-10xy = 0 \\ \\ x^2+x^2+25y^2+10x+25-10xy = 0 \\ \\ x^2+10x+25+x^2-10xy+25y^2 = 0 \\ \\ (x+5)^2+(x-5y)^2 = 0 \\ \\ Ambele~numere~din~suma~sunt~pozitive,~singura~suma~ de \\~doua~numere~pozitive~care~da ~0~este ~0+0. \\ \\ \left\{ \begin{array}{c} (x+5)^2=0 \\ (x-5y)^2=0 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x+5=0 \\ x-5y=0 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x=-5 \\ -5-5y=0 \end{array} \right \Rightarrow \\ \\ [/tex]

$\Rightarrow \left\{ \begin{array}{c} x=-5 \\ -5y=5 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x=-5 \\ y=\dfrac{5}{-5} \end{array} \right \Rightarrow\left\{ \begin{array}{c} \boxed{x=-5} \\ \boxed{y=-1} \end{array} \right|$