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Rezolvati sistemul: x*y=32
                            2(x+y)=36


Răspuns :

[tex]x*y=32=>x= \frac{32}{y} [/tex]
[tex]2( \frac{32}{y} +y)=36<=> \frac{32}{y} +y=18<=>32+y^2=18y[/tex]
[tex]<=>y^2-18y+32=0<=>y^2-16y-2y+32=0[/tex]
[tex]<=>y(y-16)-2(y-16)=0<=>(y-16)(y-2)=0[/tex]
[tex]y-16=0=>y=16[/tex] sau [tex]y-2=0=>y=2[/tex]
[tex]x= \frac{32}{y} = \frac{32}{2} =16[/tex]