One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

Rangcr897 Jul 21, 2024

#1**+1 **

We can use subsitution to our advantage.

Now, first, let's put a terms of b. From the second equation, we get that

\(a=\frac{4}{b^2}\)

Subsituting this value of x into the first equation, we get

\(\frac{4}{b^2} \cdot b^4 = 48\\\)

Now, the top and the bottom cancel out, so we have

\(4b^2 = 48\\ b^2=12\\ b=2\sqrt{3},\:b=-2\sqrt{3}\)

Thus, we find two values of b. We have

\(b=2\sqrt{3},\:b=-2\sqrt{3}\)

Thanks! :)

NotThatSmart Jul 21, 2024