system

 

One ordered pair $(a,b)$ satisfies the two equations  $ab^4 = 48$ and $a^2 = 24$.  What is the value of $b$ in this ordered pair?    

 

                                                                             

                                                                            a²  =  24    ===>    a  =  sqrt(24)

 

                                                                           ab⁴  =  48   

 

                                                              sqrt(24) • b⁴  =  48   

 

                                                                                             48          

                                                                              b⁴  =  ––––––––   

                                                                                          sqrt(24)    

 

Multiply right hand side by

sqrt(24) / sqrt(24) which is  

simply multiplying it by one.                                                   48              sqrt(24)    

                                                                              b⁴  =  ––––––––  •   ––––––––   

                                                                                          sqrt(24)         sqrt(24)   

 

 

                                                                                           48 •  sqrt(24)    

                                                                               b⁴  =   ––––––––––––     

                                                                                                   24     

 

                                                                                b⁴  =  2 • sqrt(24)    

 

                                                                                b⁴  =  sqrt(96)    

 

                                                                                b⁴  =  96^1/2     

 

                                                                                  b  =  (96^1/2)^1/4    

 

                                                                                  b  =  96^1/8      

 

From root function on scientific calculator                  b  =  1.769228    

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