ThatOnePerson

I believe it is -1.

I don't exactly understand how this is geometry, but 2+2-2 = 2.

Factoring 1763 we get that that equals 41*43. Hence, the two positive integers are 41 and 43.

I don't exactly understand what you need help with here. However, I believe that your answer in the box is correct.

It might benefit you to learn about the quadratic equation as well. It is (-b +- √b^2 - 4ac)/(2a). It is commonly used to solve quadratic equations of form ax^2 + bx + c. There are also many other ways to solve, such as completing the square. I'd recommend learning about them, they are very interesting!

Apparently 4 is a possible solution as well, according to WolframAlpha. However, I have no idea how to solve it.

First, we add the first and third equations to get -x+3z=8. Then, we multiply the first equation by two and add the third equation to that to get 3y+5z=9. Then, we subtract that from the second equation to get -3x-2y=1. Then, we add the first equation to the second and subtract the third equation from that to get 7y+6z=4. This means that we now have the equations

-x+3z=8

3y+5z=9

-3x-2y=1

7y+6z=4

Looking at the second and fourth equations, we find that y = -2 and that z = 3. Solving for x, we find that x = 1. I'll leave the checking up to you.

We can write this number as abcdcba. We know that d must be 5 since there are an odd number of fives. We now have 3 choices left for a,b, and c. Each of the permutations of those 3 choices will end up in 6 different palindromes that can be formed.

Cross multiplying, we get that 60x = 21. Dividing both sides by 60, we get that x = 7/20 = 0.35.

However, in the future, please do not post Mathcounts Trainer problems. They are meant for you to solve and you only.