Question

Fie punctele M(2,x) si N(-1,3).Determinati x apartinand lui R pentru care MN=5

Answer 1

[tex]M(2,x),N(-1,3) \\ MN=5 \\ MN= \sqrt{(-1-2)^2+(3-x)^2} \\ MN^2=(-3)^2+(3-x)^2 \\ 5^2=9+9-6x+x^2 \\ 25=18-6x+x^2 \\ x^2-6x-7=0 \\ x^2-6x-6-1=0 \\ (x-1)(x+1)-6(x+1)=0 \\ (x+1)(x-7)=0 \\ x_{1}=-1, x_{2} =7[/tex]