Question

Sa se rezolve sistemele
1.{x+y=5
xy=6

2.{x+y=11
xy=30

3.{y=2x-1
y=x^2-3x+5

4.{x+y=3
x^2+x=y

Answer 1

1. si 2. se rezolva la fel ca celelalte
x=5-y
y(5-y)-6=0
5y-y^2-6=0
y^2-5y+6=0
y^2-2y-3y+6=0
y(y-2)-3(y-2)=0
(y-3)(y-2)=0
y=3, x=5-3=2
y=2, x=5-2=3

Answer 2

1) x=2 si y=3 pentru ca 2+3=5 si 2*3=6 sau x=3 si y=2

2) x=5 si y=6 sau x=6 si y=5 pentru ca 5+6=11 si 5*6=30

3)
2x-1= x² -3x+5
0= x² -3x-2x+5+1⇒ x² -5x+6=0⇒ x² -2x-3x+6=0⇒ x(x-2) - 3(x-2)=0
(x-2) (x-3) =0⇒ x-2=0 ⇒ x=2⇒ y=2*2-1=4-1=3⇒ x=2 si y=3
sau x-3=0⇒ x=3⇒ y=2*3-1=6-1=5⇒ x=3 si y=5

4) y=3-x
x² +x=3-x⇒ x² +x+x-3=0⇒ x²+2x-3=0⇒ x²+3x-x-3=0 ⇒ x(x+3) - (x+3)=0
(x+3)(x-1) =0
x+3=0⇒ x=-3⇒ y= 3+3=6⇒ x=-3 si y=6
x-1=0⇒ x=1⇒ y=3-1=2⇒ x=1 si y=2