Recent content by A_Studen_349q

Dear brainmonsters and superbrains, have you got any new ideas?

Any ideas?

So, any new ideas?

Agrees.

Well, first, I know that "to solve a system of equations" = "find all its roots or prove that there are no roots", second, teacher told that this system has non-zero roots, third, one of my classmates tried to use some numerical methods and said he obtained positive values. So, I think that...

For any? Are you sure? Tha is f(a,c)=0? Hm... can you show it at least for one pair of variables? Well, you prooved f(x_2, x_4)-f(x_2,x_3)=f(x_3 ,x_4) but (imho) it cannot be combied with any of (1')-(3') to achieve f(a,c)=0 for any pair (a,c) of variables.

For chet and ehild: it seems you are wrong. Well, let's enumerate our eqns: \begin{align} & \sqrt{\frac{x_{1}^{2}x_{4}^{2}}{4}-{{({{x}_{1}}-{{x}_{4}})}^{2}}}-\sqrt{\frac{x_{1}^{2}x_{3}^{2}}{4}-{{({{x}_{1}}-{{x}_{3}})}^{2}}}=\sqrt{\frac{x_{3}^{2}x_{4}^{2}}{4}-{{({{x}_{3}}-{{x}_{4}})}^{2}}}\ \...

Yes, but this "linear combination" is nothing but eqn (1). Why? Well, let's enumerate our three equations of the initial system as (1), (2) and (3). We have 3 eqns and 4 vars while (1) feels lack of x2, (2) feels lack of x3, (3) feels lack of x4. The "linear combination" (let's call it (4)) you...

Nope. Roots must be real and positive. Ok, I'll wait for any ideas :)

Homework Statement A=||A(i,j)|| (i,j=1,…,n) (n>2) is a binary matrix with zero diagonal and A(i,j)=1-A(j,i) for i≠j. W=(1,1,…,1)’ is an eigenvector for matrix B=A*A. Will W be an eigenvector for matrix A too? Why? 2. The attempt at a solution Let have a look at these two statements: "a"...

Yes, but (0,0,0,0) is only a one (rather obvious) of the roots I have to find. And it gives nothing for finding all other roots.

0 gives nothing (sqare root of negative values). 1 gives nothing good either.

I tried my best though failed. First of all I tried to yield one of the variables as a function of other variables but got an equation of high (fourth) degree and stopped. Then I tried to compose (add, divide, etc) these equations to make their form easier. Failed again. Etc., etc… Well, I...

How to solve this system? \begin{align} & \sqrt{\frac{x_{1}^{2}x_{4}^{2}}{4}-{{({{x}_{1}}-{{x}_{4}})}^{2}}}-\sqrt{\frac{x_{1}^{2}x_{3}^{2}}{4}-{{({{x}_{1}}-{{x}_{3}})}^{2}}}=\sqrt{\frac{x_{3}^{2}x_{4}^{2}}{4}-{{({{x}_{3}}-{{x}_{4}})}^{2}}} \\ &...