Answer:
The value of x is [tex](+/-)\sqrt{6}[/tex]
Step-by-step explanation:
The question in English is
Find the value of x so that the distance between the given points is 2V5 units.
(2x - 1,2) and (1 + x,x + 4)
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(x+4-2)^{2}+(1+x-2x+1)^{2}}[/tex]
[tex]d=\sqrt{(x+2)^{2}+(-x+2)^{2}}[/tex]
[tex]d=\sqrt{x^2+4x+4+x^2-4x+4}[/tex]
[tex]d=\sqrt{2x^2+8}[/tex]
Remember that
[tex]d=2\sqrt{5}\ units[/tex]
substitute
[tex]2\sqrt{5}=\sqrt{2x^2+8}[/tex]
squared both sides
[tex]20=2x^2+8\\\\2x^{2}=12\\\\x^{2}=6\\\\x=(+/-)\sqrt{6}[/tex]
therefore
The value of x is [tex](+/-)\sqrt{6}[/tex]
