Sistem
{(x+y)/xy=1
{x2+y2=8
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Please briefly explain why you feel this question should be reported.
Va rugam explicate, pe scurt, de ce credeti ca aceasta intrebare trebuie raportata.
Motivul pentru care raportezi utilizatorul.
Din prima ecuatie rezulta ca![x+y=xy](https://latex.codecogs.com/gif.latex?x+y=xy)
Folosind prima ecuatie, rezulta ca
Cazul 1:
deci
. Rezulta ca
. Inlocuind in prima ecuatie:
![4=x(4-x)](https://latex.codecogs.com/gif.latex?4=x(4-x))
![4=4x-x^2](https://latex.codecogs.com/gif.latex?4=4x-x^2)
![x^2-4x+4=0](https://latex.codecogs.com/gif.latex?x^2-4x+4=0)
![(x-2)^2=0](https://latex.codecogs.com/gif.latex?(x-2)^2=0)
![x-2=0](https://latex.codecogs.com/gif.latex?x-2=0)
![x=2](https://latex.codecogs.com/gif.latex?x=2)
![y=4-x=4-2=2](https://latex.codecogs.com/gif.latex?y=4-x=4-2=2)
Cazul 2:
![x+y-1=-3](https://latex.codecogs.com/gif.latex?x+y-1=-3)
![x+y=-2](https://latex.codecogs.com/gif.latex?x+y=-2)
![y=-2-x](https://latex.codecogs.com/gif.latex?y=-2-x)
![-2=x(-2-x)](https://latex.codecogs.com/gif.latex?-2=x(-2-x))
![2=x(x+2)](https://latex.codecogs.com/gif.latex?2=x(x+2))
![x^2+2x-2=0](https://latex.codecogs.com/gif.latex?x^2+2x-2=0)
![x^2+2x+1-3=0](https://latex.codecogs.com/gif.latex?x^2+2x+1-3=0)
![(x+1)^2=3](https://latex.codecogs.com/gif.latex?(x+1)^2=3)
de unde rezulta
si ![y=-2-x=-2-(\sqrt3-1)=-2-\sqrt3+1=-1-\sqrt3](https://latex.codecogs.com/gif.latex?y=-2-x=-2-(\sqrt3-1)=-2-\sqrt3+1=-1-\sqrt3)
de unde rezulta
si ![y=-2-x=-2+\sqrt3+1=-1+\sqrt3](https://latex.codecogs.com/gif.latex?y=-2-x=-2+\sqrt3+1=-1+\sqrt3)
Din prima ec:
Avem 2 posibilitati:
sau
Solutiile sunt deci
,
si
.
Multumesc