Question

Sa se rezolve sistemul:x^2+y^2=13
x+y=5

Answer 1

x^2+y^2=(x+y)^2-2xy=25-2xy=13. 2xy=12. xy=6 de aici rezulta sol x=2 si y=3

Answer 2

x^2+y^2=13
x+y=5
(x+y)^2=5^2
(x+y)(x+y)=25
x^2+2xy+y^2=25
(x^2+2xy+y^2)-(x^2+y^2)=25-13
2xy=12
xy=12:2
xy=6
y=6/x
x+6/x=5
x*x/x+6/x-5=5-5
(x*x+6)/x=0
(x^2+6)/x=0
(x^2+6)/(5*x/x)=0
(x^2+6-5x)/x=0
x^2+6-5x=0*x
x^2-5x+6=0
Am ajuns la o ecuatie de gradul 2.
Coeficientii:
A=1
B=-5
C=6
Δ=b^2-4ac=-5^2-4*1*6=25-24=1
Δ>0
x=(5+/-√1)/2
x=5+/-1)/2
x1=(5+1)/2=6/2=3
x2=(5-1)/2=4/2=2
y=5-x
y1=5-3=2
y2=5-2=3
x,y∈(3;2);(2;3)