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For what values of a does the equation a+x=1+xa^2 have no solution?

 Nov 2, 2019
 #1
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a+x=1+xa^2   rearrange as

 

a^2x - x  =  a - 1

 

x (a^2 - 1)  =  (a - 1)

 

x ( a + 1) (a - 1)  = (a - 1)         divide both sides by (a - 1)

 

x ( a + 1)  =   1                      divide both sides by  (a + 1)

 

x  =   1  / ( a + 1)

 

This will have no solution when  a  =  -1   [ since we cannot divide by 0  ]

 

 

cool cool cool

 Nov 2, 2019

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