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One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 b^5 = 72$. What is the value of $b$ in this ordered pair?

 Jul 31, 2023
 #1
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We can divide the two equations to get:

a^2/b = 2

Squaring both sides, we get:

a^4/b^2 = 4

Substituting ab^4=48, we get:

48/b^2 = 4

Solving for b2, we get:

b^2 = 12

Therefore, b = sqrt(12) = 2*sqrt(3).

 Jul 31, 2023
 #2
avatar+746 
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This is either GPT generated or the wat troll. How is 72 / 48 2?

history  Jul 31, 2023
 #3
avatar+183 
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We divide the equations to get \(ab=\frac32\), then \((ab)b^3=48 \implies b^3 = 32\), so \(b=2\sqrt[3]4\). 

 Aug 1, 2023

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