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 !!
\(a = 4 \sqrt[3]{4}, b = 2 \sqrt[3]{3}\)
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
