A point (3*sqrt(5), d + 6) is 3d units away from the origin. What is the smallest possible value of d?
+128475 Using the square of the distance formula
(3sqrt (5))^2 + (d +6)^2 = (3d)^2 simplify
45 + d^2 + 12d + 36 = 9d^2
Rearrange as
8d^2 -12d - 81 = 0
Using the quad formula
12 ± sqrt ( 144 - 4 * 8 (-81) )
________________________ =
2* 8
12 ± sqrt ( 2736)
______________ take the positive answer
16
12 + sqrt (2736)
_______________
16
12 + 12 sqrt (19)
______________
16
(12/16 ( 1 + sqrt (19) ) =
(3/4) ( 1 + sqrt (19) ) = d
