Question

11. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ____​

Answer 1

Step-by-step explanation:

given

A=(X,-1)

B=(3,2)

AB=5Units

$distance \: between \: two \: points = \: \sqrt{(x_{2} - x_{1})^{2} + (y_{2} -y_{1})^{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 = \sqrt{(3 - x)^{2} + (2 - ( - 1))^{2}} \\ 5= \sqrt{(9 + {x}^{2} - 6x + 9}$

squareing on both sides

$5 ^{2} = (\sqrt{(9 + {x}^{2} - 6x + 9} )^{2} \\ 25 = 18 + {x}^{2} - 6x \\ 7 = {x }^{2} - 6x \\ { x}^{2} - 6x - 7 = 0 \\ {x }^{2} - 7x + x - 7 = 0\\x(x - 7) + 1( x - 7) = 0 \\ (x + 1)( x - 7) = 0$

=(x + 1)( x - 7) = 0

(x + 1)= 0. | ( x - 7) = 0

X=-1. |. X=7

therefore X= -1,7