Question

One ordered pair (a,b) satisfies the two equations ab^4 = 12 and a^5 b^5 = 7776. What is the value of 'a' in this ordered pair?

Answer 1

a = 4.762203156

Explanation:

Given:

ab^4 = 12 and a^5b^5 = 7776

Making the equations a subject of a;

a = 12/b^4 and a^5 = 7776/b^5

Finding fifth root on both sides of equation two;

a =
`\sqrt[5]{7776}`/b

You will get a = 6/b

Equating the two equations;

12/b^4 = 6/b

Multiplying both sides by b^4 gives:

b =
`\sqrt[3]{2}` = 1.25992105

We had that a = 12/b^4 so;

a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156