Question

Find x so the distance between (x,2) and (1,5) is 13.

Answer 1

`A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\|AB|=√((x_2-x_1)^2+(y_2-y_1)^2)\\----------------\\√((1-x)^2+(5-2)^2)=13\\(1-x)^2+3^2=169\\(1-x)^2=169-9\\(1-x)^2=160\\1-x=\pm√(160)\\-x=\pm√(16*10)-1\\-x=\pm4√(10)-1\\\boxed{x=1\pm4√(10)}`



`√((1-x)^2+(5-2)^2)=√(13)\\(1-x)^2+3^2=13\\(1-x)^2=13-9\\(1-x)^2=4\\1-x=\pm\sqrt4\\-x=\pm2-1\\-x=-2-1\ or\ -x=2-1\\-x=-3\ or\ -x=1\\\boxed{x=3\ or\ x=-1}`