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one ordered pair (a, b) satisfies the two equations \(ab^4=384\) and \(a^2b^5= 4608\). what is the value of a in this ordered pair?

 

thank y'all so much !!

 Dec 24, 2019
 #1
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\(a = 4 \sqrt[3]{4}, b = 2 \sqrt[3]{3}\)

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 Dec 24, 2019
 #2
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ab^4  =  384    

a^2b^5 =  4608

 

Divide the second  equation by the  first

 

ab  = 12    ⇒    b = 12/a

 

Sub this into the  first equation

 

a [12/a]^4  = 384

 

12^4 / 384  = a^3

 

a = ∛54

 

a = 3∛2

 

b  =  12 /[3∛2]=    4 /∛2  =  4 * ∛4 / 2 =  2∛4

 

 

 

cool cool cool

 Dec 24, 2019

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