Question

sa se determine m apartine de R astfel incat dinstanta dintre punctele A(2,m) si B(m,-2) sa fie =4

Answer 1

$A(2,m) \\ B(m,-2) \\ AB=4 \\ \sqrt{(m-2)^2+(-2-m)^2} =4 \\ (-2-m)^2= [-(2+m)]^2=(2+m)^2 \\ \sqrt{(m-2)^2+(2+m)^2}=4 |^2 \\ (m-2)^2+(2+m)^2=16 \\ m^2-4m+4+4+4m+m^2=16 \\ 2 m^2+8=16 \\ 2m^2=8|:2 \\ m^2=4 \\ m=2$
m∈R