Question

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?

Answer 1

Answer: a = 3∛2

Step-by-step explanation:

ab⁴ = 384     --> a = 384/b⁴

Substitute a = 384/b⁴ into the second equation to solve for "b".

   a²b⁵ = 4608

$\bigg(\dfrac{384}{b^4}\bigg)^2\cdot b^5=4608\\\\\\\dfrac{147,456b^5}{b^8}=4608\\\\\\\dfrac{147,456}{b^3}=4608\\\\\\\dfrac{147,456}{4608}=b^3\\\\\\32=b^3\\\\\\\sqrt[3]{32} =b\\\\\\2\sqrt[3]{4} =b$

Substitute b = 2∛4 into the first equation to solve for "a".

ab⁴ = 384

a(2∛4)⁴ = 384

        a  = 384/(2∛4)⁴

        a = 24/4∛4

           = 6/∛4

           = 6(∛2)/2

           = 3∛2