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A point (3*sqrt(5), d + 6) is 3d units away from the origin. What is the smallest possible value of  d?

 Dec 17, 2020
 #1
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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

 

 

cool cool cool

 Dec 17, 2020

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