Răspuns:
[tex]M(2,x); N(-1,3)[/tex]
[tex]|MN|=\sqrt{(xn-xm)^2+(yn-ym)^2}[/tex]
[tex]=\sqrt{(-1-2)^2+(3-x)^2}[/tex]
[tex]=\sqrt{(-3)^2+9-6x+x^2}[/tex]
[tex]=\sqrt{x^2-6x+18}[/tex]
Stim ca MN = 5 =>
[tex]\sqrt{x^2-6x+18}=5 |*()^2[/tex]
[tex]|x^2-6x+18|=25[/tex]
Caz 1:
[tex]x^2-6x+18=-25[/tex]
[tex]Delta=(-6)^2-4*1*43=36-172=-136 => x[/tex]∉R
Caz 2:
[tex]x^2-6x+18=25[/tex]
[tex]x^2-6x-7=0[/tex]
[tex]x^2+x-7x-7=0[/tex]
[tex]x(x+1)-7(x+1)=0[/tex]
[tex](x+1)(x-7)=0=>x1=-1 ; x2=7[/tex]
Solutiile sunt x1 = -1 si x2 = 7
