Question

The arithmetic mean between two numbers is 75 and their geometric mean is 21. Find the numbers.

Answer 1

We can just set up a equation. Let the 2 numbers be a and b.

(a+b)/2=75

Simplify first equation a+b=150

Now second equation

`\sqrt[2]{a*b}`=21

Now we can simplify that getting

ab=441

Let's isolate a in the first simplified equation.

a=150-b

Now let's substitute into second simplified equation.

(150-b)*b=441

Now we can solve.

-b^2+150b=441

b^2-150b+441=0

Now factor, this might be hard considering how good are you at spotting the factors.

(b-3)(b-147)=0

b=3 or 147

Respectively a=147 or 3 in the opposite order.

Hope this helps!

Answer 2

147 and 3

Explanation:

This means that their sum is 75 * 2 = 150 and their product is 21 * 21 = 441.

The two numbers that work for this is 147 and 3.

The way you can find this is by making a list of factors of 441 and then seeing which ones add up to 150