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The parabolas defined by the equations y = -x^2 - x + 1 and y = x^2 - 3x - 3 intersect at points (a,b) and (c,d), where c >= a. What is c - a? Express your answer as a common fraction.

 Aug 1, 2022
 #1
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Set the equations equal

 

x^2 - 3x - 3 =  -x^2  - x  + 1              rearrange as

 

2x^2 - 2x - 4   =  0              divide through by 2

 

x^2 - x  - 2   =  0

 

(x - 2) ( x +1)   = 0

 

x -  2   = 0                 x + 1  = 0

 

x  = 2  = c                 x =  -1  =   a

 

c - a =   2 -  (- 1 )  =   3

 

 

cool cool cool

 Aug 1, 2022

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