Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I need to solve the following system of $(x,y)$: \begin{cases} 3y^3+3x\sqrt{1-x}=5\sqrt{1-x}-2y\\ x^2-y^2\sqrt{1-x}=\sqrt{2y+5}-\sqrt{1-x} \end{cases}

share|cite|improve this question
    
Substitute $z=\sqrt{1-x}$, $u=\sqrt{2y+5}$. This will give you a polynomial in $z$. – Michael Hoppe Oct 3 '13 at 12:27
    
How about $u$? I have already done but there is no more results. Can you explain more clearly? Thanks. – Dinh Anh Thi Oct 3 '13 at 13:21

you can try the solve it numerically first with newton algorithm:

$$ f(x,y) = (3y^3-2x\sqrt{1-x}-2y, x^2+(1-y^2)\sqrt{1-x}-\sqrt{2y+5}) $$

$$ (x_{n+1}, y_{n+1}) = (x_n,y_n) +Df(x_n,y_n)^{-1}.f(x_n,y_n) $$

with $$(x_0,y_0) =(0,0) $$

share|cite|improve this answer
2  
Oh, my! This looks (looks ...) as discouraging hopeless as the original equations...or maybe more! – DonAntonio Oct 3 '13 at 12:12
    
It's really quite complicated. Actually, there exists a method which can solve this system more simply but I can't find now. – Dinh Anh Thi Oct 3 '13 at 12:29

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.