Given:
The distance between the two points (11, 1) and (x, 17) is 20.
To find:
The possible values of x.
Solution:
Distance formula is:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using this formula, the distance between (11, 1) and (x, 17) is
[tex]D=\sqrt{(x-11)^2+(17-1)^2}[/tex]
[tex]20=\sqrt{x^2-22x+121+(16)^2}[/tex]
[tex]20=\sqrt{x^2-22x+121+256}[/tex]
Taking square on both sides.
[tex]400=x^2-22x+377[/tex]
[tex]0=x^2-22x+377-400[/tex]
[tex]x^2-22x-23=0[/tex]
Splitting the middle term, we get
[tex]x^2-23x+x-23=0[/tex]
[tex]x(x-23)+(x-23)=0[/tex]
[tex](x-23)(x+1)=0[/tex]
Using zero product property, we get
[tex]x=-1,23[/tex]
Therefore, the possible values of x are -1 and 23.
