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Suppose that a(x+b(x+3))=2(x+6) for all real values of x. Determine a+b.

 Dec 9, 2018

Best Answer 

 #1
avatar+18360 
+2

a(x+b(x+3))=2(x+6)      expand

a(x + bx + 3b) =2x+12

ax + abx + 3ab= 2x +12       equate 'like' terms on both sides of the equations

 

ax(1+b) =2x      and   3ab=12 

a(1+b) = 2                    ab = 4

 

a = 2/(1+b)     Sub this into the second equation    ab=4

                                                                                2/(1+b) *b = 4

                                                                               2b/(1 +b) = 4

                                                                               2b = 4(1+b)

                                                                                  b = 2+2b

                                                                                  -b=2                        so b = -2   a= 2/(1+(-2)) = -2

 

 a+b = -2 + -2 = -4

 Dec 9, 2018
 #1
avatar+18360 
+2
Best Answer

a(x+b(x+3))=2(x+6)      expand

a(x + bx + 3b) =2x+12

ax + abx + 3ab= 2x +12       equate 'like' terms on both sides of the equations

 

ax(1+b) =2x      and   3ab=12 

a(1+b) = 2                    ab = 4

 

a = 2/(1+b)     Sub this into the second equation    ab=4

                                                                                2/(1+b) *b = 4

                                                                               2b/(1 +b) = 4

                                                                               2b = 4(1+b)

                                                                                  b = 2+2b

                                                                                  -b=2                        so b = -2   a= 2/(1+(-2)) = -2

 

 a+b = -2 + -2 = -4

ElectricPavlov Dec 9, 2018

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