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

 May 9, 2020
 #1
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a·b4  =  384     and     a2·b5  =  4608     --->     a2·b5​ / a·b4  =  4608 / 384     --->      a·b  =  12

 

I tried various whole number values for a and b; none worked.

 

Square roots won't work either.

 

I tried  cube roots, giving one value the cube root of 2 and the other the cube root of 4.

 

Finally:     a  =  3·21/3     and     b  =  2·41/3

 May 10, 2020

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