Question

Fie A(2;3) si B (4;x). Determinati x care apartine multimi numerelor rationale astfel incat AB=2radical din 5

Answer 1

AB=rad((xb-xa)^2+(yb-ya)^2)
AB=rad((4-2)^2+(x-3)^2)
2rad5=rad(4+x^2-6x+9)
4*5=x^2-6x+13
x^2-6x-7=0
x^2-7x+x-7=0
x(x+1)-7(x+1)=0
(x+1)(x-7)=0
x+1=0==>x=-1
x-7=0==>x=7
x apartine{-1;7}