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Let a and b be real numbers such that a + b = -1. Compute a^2 - b^2 + 3a + b.

 Jul 12, 2021
 #1
avatar+137 
+2

Note the entire expression is 2(a + b), so substitution gives a^2 - b^2 + 3a + b = -2.

 Jul 12, 2021
 #2
avatar+121065 
+2

a^2  - b^2   +  3a   +  b

 

(a + b) (a  - b)  +  3a  + b

 

(-1)(a - b)   + 3a  + b  =

 

-a + b  +  3a  +  b  =

 

2a + 2b  = 

 

2 ( a + b)   =

 

2 (-1)    =  

 

-2.......just  as HSD  found  !!!!!!

 

 

cool cool cool

 Jul 12, 2021
 #3
avatar+137 
+1

GREAT SOLUTION

HighSchoolDx  Jul 12, 2021

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