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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?

 Jul 9, 2020
 #1
avatar+111628 
+1

I rarely if ever answer questions that have not been asked properly, all those $ signs have no meaning.

Plus you will have a slightly higher chance of getting good answers if you become a member. (it is free and easy) 

If you make a good impression as a member it becomes almost a given that you will get a good answer.

 Jul 9, 2020
 #3
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-1

All the dollar signs are for latex, most likely from aops, so next time don't give out complete answers but crucial hints that can help them b/c the whole reason for the homework is so that they can reinforce their education but just getting the answer doesn't help at all.

Guest Jul 9, 2020
 #4
avatar+111628 
-1

Yes the dollar signs are from latex that is blatantly obvious.

I am fed up with hearing about aops.

This latex could be from anywhere!

 

Do you think aops is the only teaching institute that puts questions online in LaTex.

That is rediculous!

Melody  Jul 10, 2020
 #2
avatar+8352 
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\(ab^4 = 384\\ a^2 b^5 = 4608 \)

 

Considering the second equation: 

\(ab^4 \cdot ab = 4608\\ ab = \dfrac{4608}{384} = 12\)

 

Considering the first equation:

\(ab^4 = 384\\ ab\cdot b^3 = 384\\ b = \sqrt[3]{\dfrac{384}{12}} = 2\sqrt[3]4\)

 

Substituting directly gives \(a =3 \sqrt[3]{2}\)

 Jul 9, 2020

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