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1. The distance between the points (x,21) and (4,7) is 10sqrt2 Find the sum of all possible values of x.

 May 5, 2020
 #1
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Let's  just get  the square of the distance formula

 

Note 10sqrt (2)  =  sqrt (200)

 

( 4 - x)^2  + (21 - 7)^2  =  (sqrt 200)^2         expand  and simplify

 

(x - 4)^2  + 14^2   = 200

 

(x - 4)^2  + 196  = 200

 

(x - 4)^2  =   4        take  both roots

 

x - 4  =  sqrt (4)        and     x - 4  =  -sqrt (4)

x - 4  =  2                            x - 4  =  -2

x  = 6                                  x  =  2

 

So...the sum    = 6 + 2    =  8

 

 

cool cool cool

 May 5, 2020

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