Ehrlich

c + o= u 
u + n= t 
t + c = s
o + n + s = 12

u+n=(c+o)+n=t

t+c=(c+o+n)=c=s

o+n+s=o+n+(c+o+n+c)=(c+o+n)*2+t*2=12  | divide by 2=

t=6

If you want to solve an equation That has an absolute value in it, You can (and should) seperate your answer to two or more different answers. Heres an example:

lets say we want to solve |x+4|=5. Lets seperate our answer to two different cases:

1. x+4 is bigger than 0, meaning the equation is x+4=5 (x=1)

2. x+4 is smaller than 0, meaning the equation is -x-4=5 (x=-9)

i hope i helped!

We are given that (a²+b²)/(ab+1) is an integer (lets call the unteger c). we also know that a and b are integers.

(a²+b²)/(ab+1)=c   | subtract a² (a² is an integer, meaning c-a² is an integer too)

(b²-a³b)/(ab+1)=b*(b-a³)/(ab+1). b and ab+1 are coprime integers.

proof: suppose there is a number n that divides b. that means it also divides ab. So it will divide ab+1 only if 1 is divisibly by it. therefore, that number must be 1. So the numbers are coprime. That means (b-a³) is divisible by ab+1.

The only thing i can add is that b<=a³. 

You dont seem to try the questions you post, because you post a question every 30 minutes. Are you even trying your homework or do you want just want other people to do it for you?

edit: >:(

John von neumann, one of the most brilliant mathematicians ever, once said:

"In mathematics you don't understand things. You just get used to them"

So no, you are not stupid

The newton-Raphson method is meant to give you a close answer, not the exact answer. It is usually used to solve other equations, like sin(x)=2x, not polynomials, because if im not mistaken there is a way to solve polynomials.

but ill try to solve it using that method anyways:

well, the first thing you need to do, is find a value that gets "close enough" to the answer. Well, that term is not very specific, And i dont have any other way to explain it, but we need to get a pretty close answer, or it wont work.

Ill explain why:

There is a function, and we want to find its roots. imagine the function has "ups" and "downs", hills and ravines. When we use the method, We get an endless series of answers, getting closer and closer to the root of the function. But we need to make sure we got inside the ravine, or one of the members of the series might "get out" and start getting further and further, meaning we wont get the accurate solution we need :(.

So, Lets find a close value: first, lets find the derivative of the function (We will use it later):

f'(x)=(x¹¹+3x¹⁰+x⁹+x-15)'=11x¹⁰+30x⁹+9x⁸+1.

1.11 is a pretty close value.

I spoke earlier about an endless series. What you are supposed to do is pick a high integer for n (You can use any computer program for that) and calculate the n^th term of the series where:

x₀=1.11=the number we chose.

x_n+1=x_n-f(x_n)/f'(x_n)

that means x₁=x₀-f(x₀)/f'(x₀)=1.11-f(1.11)/f'(1.11)

Heres what wikipedia has to say about that subject:

https://en.wikipedia.org/wiki/Newton%27s_method

But You dont HAVE to use that method. There is a nice method that can help you find the rational solutions of the equation, meaning it can help you factorize the equations (i already posted it):

STEP ONE:

we have the polynomial a₀+a₁*x+a₂*x²+a₃*x³+........+a_n*xⁿ=0. We need to multiply the polynomial by a number in a way that all coefficients will be whole numbers. Sometimes we cant do it. sometimes we can.

STEP TWO:

find all of the whole divisors of a_n and a₀ (including the negative divisors). lets call the set of the divisors of a₀ A and the set of the divisors of an B. there are k divisors in A and m divisors in B.

Every rational root of the polynomial=A_i/B_j,  A_i is a member of A and B_j is a member of B, meaning every rational root can be expressed using one divisor from A divided by one divisor from B).

STEP THREE

Check for every two divisors (one from A and one from B) if A_i/B_j is a root. after a finite amount of time (unless your calculator is broken) you'll have every rational root of the polynomial.

Im not 100% sure i understood your question, but if i did, then the answer is no (There are no integers x and y that satisfy 3*x²=y²).

But this is not going to help you determine whether perfect cuboids exist. That question is a little harder than that.

http://wikirhymer.com/words/death

earth?

Someone asked me to answer this, but i dont understand what you're trying to say.

Theres nothing "special" about this number. That was the first guest's question, and i answered it.