Question

find the value of,x1 if the distance between the point (x1'2) and (3'4) be 8

Answer 1

$using \: distance \: formula \\ \sqrt{ {(x1 - 3)}^{2} + {(2 - 4)}^{2} } = 8 \\ squaring \: both \: sides \\ {(x1 - 3)}^{2} + 4 = 64 \\ x1 - 3 = \sqrt{60} \: or \: - \sqrt{60} \\ x1 = 3 + \sqrt{60} \\ or \: 3 - \sqrt{60}$

Answer 2

let P=(x1,2) and Q =(3,4)
thus distance between points can be calculated by distance formula
distance between and Q=8
√{(3-x1)^2+(4-2)^2}=8
(3-x1)^2+4=64
9+x1^2-6x1=60
(x1)^2-6x1-51=0
x={6+-√(36+204)}/2
=(6+-√240)/2
=(6+-4√15)/2
=3+-2√15