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

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

=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!

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