0

I am trying to find the values of x, y and z having these equations. a, b and c are constants. $$ \begin{cases} a = (\frac y x)^{1/2} \cdot \frac {x+y} x \\ b = (\frac z x)^{1/2} \cdot \frac {z+x} x \\ c = (\frac y z)^{1/2} \cdot \frac {y+z} z \end{cases} $$ I have no idea how to find values of x, y and z. I have tried to solve them by multiplication, division by all I get in return is another set of equations.

Thanks for the help.

Pro
  • 71
  • Perhaps you have a typo in the denominator in the first line. – Kavi Rama Murthy Aug 25 '21 at 09:28
  • Yes it is, I have corrected. Thanks – Pro Aug 25 '21 at 09:32
  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Aug 25 '21 at 09:41
  • Firstly, I am no major in Mathematics, a chemist. I am stuck at a problem like this, which I do not know how to solve. Even I do not know what type of problem is this. I have tried to solve it in pen and paper, but to no avail. This was my try. I thought I could ask for some help here. – Pro Aug 25 '21 at 09:45
  • Hmm... your equations looks strange and I suspect there are more typos. The 1st and 2nd equations are cubic equations in $\sqrt{y/x}$ and $\sqrt{z/x}$. In principle, you can express $y/x$ solely in terms of $a$, $z/x$ solely in terms of $b$. The 3rd equation becomes either redundant or inconsistent.... – achille hui Aug 25 '21 at 09:46
  • @achillehui I have checked again. No typos. – Pro Aug 25 '21 at 09:52
  • 1
    In this case, you have 3 equations of the form $t^3 + t = p$. If you throw the command Solve[ t^3 + t = p, {t}] to WA, it will give you a complicated expression for the 3 roots of polynomial. Only the first one is real and the one you need $$t = \frac{\sqrt[3]{\sqrt{3} \sqrt{27 p^2 + 4} + 9 p}}{\sqrt[3]{2},3^{2/3} } - \frac{\sqrt[3]{\frac23}}{\sqrt[3]{\sqrt{3} \sqrt{27 p^2 + 4} + 9 p}}$$ – achille hui Aug 25 '21 at 10:10
  • This is a strange problem. Being a chemist, may be you could tell if all $(a,b,c,x,y,z)$ are positive. – Claude Leibovici Aug 25 '21 at 11:45
  • From the intuition, x, y, z should come positive. From the calculated values, a, b or c may be negative. – Pro Aug 25 '21 at 13:28

0 Answers0