Explicație pas cu pas:
1. x²+y²+19=4(x-2y) =>
x²+y²+19=4x-8y => x²-4x+y²+8y+19=0 =>
x²-4x+4+y²+8x+15=0 =>
(x-2)²+y²+8x+16-1=0 =>
(x-2)²+(y+4)²=1
<=> (x-2)²<=1 => -1<=x-2<=1 => 1<=x<=3 =>
x€[1,3]
(y+4)²<=1 => -1<=y+4<=1 => -5<=y<=-3 =>
y€[-5,-3]
Observam ca x-pozitiv si y-negativ =>
x>y
2. a=V(x²+4x+4)+V(x-5)² =>
a=V(x+2)²+|x-5| =>
a=|x+2|+|x-5|
x€[-2,5] => -2<=x<=5 =>
x+2>=0 si x-5<=0 =>
a=x+2+5-x=> a=7€N
3. (x+2)/(x-1) €N <=> x-1|x+2 dar x-1|x-1
Le scadem:
x-1|x+2-x+1 =>x-1|3 =>x-1€D3 in Z =>
x-1€{-3,-1,1,3} =>
x€{-2,0,2,4} x€N => x€{0,2,4} => A={0,2,4}
-1<=(4x-6)/2<5 => -2<=4x-6<10 =>
4<=4x<16 => 1<=x<4 => x€[1,4)
=> B=[1,4)
AnB={0,2,4}n[1,4)=2
