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One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

 Sep 24, 2024
 #1
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                                                  ab4 = 48           (eq 1)    

                                                  ab2 = 4             (eq 2)    

 

solve (eq 2) for a                       a = 4 / b2     

 

sub a back in to (eq 1)               (4 / b2) • b4  =  48    

                                                   (b4 / b2)  =  48 / 4    

                                                             b2  =  12   

                                                               b  =  2 • sqrt(3)    

 

The problem doesn't ask for a     

 but sub b2 back in to (eq 2)             a • 12  =  4    

                                                                a  =  4 / 12    

                                                                a  =  1 / 3     

.   

 Sep 28, 2024

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