Solving simulataneous equation using maxima? - maxima

Question

Hi I want to solve three equation, please find the details in picture. I want to find the value of alpha, h and Q in terms of alpha and h how do i do this using Maxima?
[B1=\frac{{{h}^{2}}}{\mathit{Qs}}]
[B2={{h}^{2}}+\alpha+1]
[B3=\frac{1}{\mathit{Qs}}]
[B0={{h}^{2}}]
[C2=\frac{{{h}^{4}}}{{{\mathit{Qs}}^{2}}}-2{{h}^{2}}\,\left( {{h}^{2}}+\alpha+1\right) =0]
[C4={{\left( {{h}^{2}}+\alpha+1\right) }^{2}}-\frac{2{{h}^{2}}}{{{\mathit{Qs}}^{2}}}-2{{h}^{2}}=0]
[C6=\frac{1}{{{\mathit{Qs}}^{2}}}-2\left( {{h}^{2}}+\alpha+1\right) =0]
algsys([C2,C4,C6],[h,alpha,Qs]);?????

Answer 1

I see that by just adding QS to the list of variables to solve for, I get some solutions. I didn't check them. Some of them may be redundant, I didn't check that either.
(%i20) algsys ([C2, C4, C6], [h, alpha, QS]);
(%o20) [[h = -1,alpha = -(2^(3/2)-2)/(sqrt(2)-2),QS = sqrt(2-sqrt(2))/2],
[h = 1,alpha = -(2^(3/2)-2)/(sqrt(2)-2),QS = sqrt(2-sqrt(2))/2],
[h = -1,alpha = -(2^(3/2)-2)/(sqrt(2)-2),QS = -sqrt(2-sqrt(2))/2],
[h = 1,alpha = -(2^(3/2)-2)/(sqrt(2)-2),QS = -sqrt(2-sqrt(2))/2],
[h = -1,alpha = -(2^(3/2)+2)/(sqrt(2)+2),QS = sqrt(sqrt(2)+2)/2],
[h = 1,alpha = -(2^(3/2)+2)/(sqrt(2)+2),QS = sqrt(sqrt(2)+2)/2],
[h = -1,alpha = -(2^(3/2)+2)/(sqrt(2)+2),QS = -sqrt(sqrt(2)+2)/2],
[h = 1,alpha = -(2^(3/2)+2)/(sqrt(2)+2),QS = -sqrt(sqrt(2)+2)/2]]

Answer 2

Try replacing h^2 with a single variable, say h2 (and replace h^4 with h2^2).
Try simplifying the equations with expand and/or ratsimp.
In solve(eqns, vars), the variables vars are the ones you are trying to solve for. So I think you want alpha, h, Q (well, actually alpha, h2, Q if you follow my previous advice).
Finally, PLEASE paste your input and output into the question instead of linking to an image, which makes it much more difficult for someone else to try working with your equations.