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Find all values  for which there exists an ordered pair  satisfying the following system of equations:
a+ab^2=40b

a-ab^2=-32b

List only the values for a

 Jul 22, 2022
 #1
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The solutions (a,b) are (12,3) and (-12,-3), so the possible values of a are 12 and -12.

 Jul 22, 2022
 #2
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a + ab^2 =  40b       (1)

a - ab^2  = 32b         add these equations

 

2a  =  72b

 

a  = 36b    (2)

 

Sub   (2) into (1)

 

36b + (36b)b^2  =  40b

 

36b^3   =  4b

 

36b^3  - 4b  =  0

 

4b (  9b^2  - 1)  = 0

 

4b ( 3b -1)  (3b + 1)  = 0

 

4b = 0         3b  -1   = 0         3b + 1  = 0

b = 0            b  =1/3              b = -1/3

 

a = 36 (0)  =  0

 

a = 36 (1/3)   =  12

 

a = 36 (-1/3)   = -12

 

 

cool cool cool

 Jul 22, 2022

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