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\(\begin{align*} a + ab^2 & = 40b, \\ a - ab^2 & = -32b. \end{align*}\)

Find all values for a

 Oct 22, 2017
 #1
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+1

a + ab^2  = 40b

a -  ab^2 = -32b

 

Add the equations

 

2a = 8b   →  a = 4b  

 

Sub this into the first equation

 

4b + 4b^3  =   40b       divide through by 4

 

b + b^3 =  10b     rearrange

 

b^3 - 9b  =  0     factor

 

b ( b^2 - 9)  = 0    →    b = 0   or   b = -3  or b = 4

 

So.....a = 4b  =   

 

0 ,  -12  or  12

 

 

cool cool cool

 Oct 22, 2017

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