CalculatorUser

Satisfying solution by Melody here!

You have to make sure it satisfies 2x + 3y = 5

How can you be sure xy is equal to 5?

Thanks Omi!

Strange, AoPS has some wrong answers....

Can you solve using this informaion?

Guest's solution doesn't use calculus, it uses triginometry.

But you get what I mean.

A simple knowledge of 30 60 90 well help!

its a ti-84.

except the one in the picture is a rando from google images.

Very nice solution!

This is why there is a controversy to whether someone should learn calculus at a young age.

In my opinion, it is not good to learn calculus. Because the extra knowledge my blur your vision on seeing simple solutions.

The internet is the source of all my dark magic, without it I will be powerless.

Here is my attempt:

Good job on finding \( 0=-3j+jk-3k\) guys, we can work from here?

We factor:

\(0=j(-3+k)-3k\)

Simplifies to:

\(0=j(k-3)-3k\)

We add 9 to both sides, this allows us to factor better:

\(9=j(k-3)-3k+9\)

We factor once again

\(9=j(k-3)-3(k-3)\)

We then simplify:

\(9=(j-3)(k-3)\)

Now that we have a binomial expression, we can list the factors of 9 to guess solutions.

1 and 9

3 and 3.

So for 1 and 9, we set them equal

\(j-3=1\)

\(k-3=9\)

Solving this, we get J=4 and k=12, since they can be reversed, the values of K and be 4 or 12.

Now we solve 3 and 3

\(j-3=3\)

\(k-3=3\)

Solving this, we get J=6 and K=6, since they can be reversed, the values of K can only be 6.

So the possible values for K can be 4, 6, and 12.

The sum of that is \(\boxed{22}\)

A factor of 9 is also -3 and -3. But do you know why it doesn't work?