VVoidSmiley69

Thanks Hugo, it was right! Mr.Ruiz is really good. Also, I am try to prepare for AMC 10, since I only got a 97.5 last time. Do you have any reccomendations of what books to buy, I was going to buy Volume 1 but idk if thats the best option. :D

Alcumus my guy and I am not in Intro to geometry. I am only in intro to algebra B. I am just trying to prepare for AMC 10 so please dont bully me.Proof:

-2 as well, are there any more?

+/- \(i\sqrt{8}\)

I am new to matrices so I might be wrong. 

Firstly we multiply a and b. For the first element (the top one on a) we multiply that by every single element in b, then we do that for the second element in a, then for the third, hence we get.

0+0+0=0

-1*2+0+-1*20=-22

10*2+0+10*20=220

Then we add all this up to give us 198.

Next we do the same process except for b. Thus,

2*4+2*1+2*30= 70

0+0+0=0

20*4+20*1+20*30=700

Then we add all that up to get 770. So as of right now we have 770 + 198.

Next we do the same process for a again but to c, hence we get

0+0+0=0

-1*4+-1*1+-1*30=-35

10*4+10*1+10*30=350

350-35=315

Now, we have 198+770+315, which gives us 1283.

I am most likely wrong :).

Thanks Alan :)

AOPS directed us in the using vieta (-b/2a) or the average of the roots which is close to the idea of vietas. I am pretty sure it is correct, I ca not see how anything else is the maximum, but I am not the smartest so I could wrong as well.

I am new to quadratic optimzation so I just tried out a trick and it worked lol. I learned the way of expanding and such, but I wanted to try completing the square, sorry I could not help you.

Sorry I am not 100% how to explain this but basically by completing the square, we can eventually put the equation in vertex form, which in this case will give us the maximum. In this the equation became -1(x+27.5)^2+765.25. So we know that 765.25 is the maximum.

Essentially, we just complete the square so we can easily fine the vertex through vertex form.

Yup I get. Thanks for this post, it really made cheater realize their loss of learning. They are also losing money by only looking for answers, hope they can learn.

It means to bring the variable on one side and to the constants on the other side essentially.

I will admit I have done this a few times, but i am mostly looking for the steps, I really don't care if I get 5/7 or a 3/7, I only want to learn the content, and sometimes teh message boards dont help. I think thats why many kids come here including myself sometimes come here to ask for help, while others only want answers. I understand your point, maybe people could ask for starting points instead of direct answers? 

For the maximum, I started off by adding up all the integers. 1+2+3...+10=55. 

So with that I gave a variable to each group, x and y.

Thus, x+y=55, then I switched that to a slope intercept form, so y= -x+55

So that gave me P= y * x, which I then simplified to P= x* (-x+55), which became -(x^2-55x)

Then we can complete the square to get -(x^2-55x+765.25), and that simplified is -(x-27.5), so 27.5* 27.5 will give us the highest number, but since we only have intergers we can go +1 and -1 to get 27*28 and that will equal 756.

How can I find the minimum with completing the square? Thats the part I dont understand.

Thanks Melody, this answer als provides me a different insight the problem. 

Thanks a lot Geno, I clearly understand the problem now. :)

Sorry I am new to Latex, I will try not to do it again :)