Hello mathematicians,

I am a student of musical composition and I need to solve the following problem for one of my pieces. I worked on it for a long time but I have not taken enough advanced algebra to solve it.

I am looking for the list: $\displaystyle W=((x_{0},n_{0},q_{0},s_{0}),(x_{1},n_{1},q_{1},s_ {1}),(x_{2},n_{2},q_{2},s_{2}),...(x_{w},n_{w},q_{ w},s_{w}))$

such that

1. $\displaystyle \sqrt{x_{i}+\mathit{n_{i}q_{i}}}=58\frac{9}{16}+\s qrt{x_{i}}$

2. $\displaystyle \sqrt{x_{i}+q_{i}}=11\frac{3}{16}+\sqrt{x_{i}}$

3. $\displaystyle \sqrt{x_{i}+\mathit{n_{i}q_{i}}}=s_{i}+\sqrt{x_{i} +(n_{i}-1)q_{i}}$

4. $\displaystyle 2\le s_{i}<11\frac{3}{16}$

5. $\displaystyle s_{i}\in \mathbb{R}$

6. $\displaystyle n_{i}\in \mathbb{Z}$

7. $\displaystyle x_{i}\in \mathbb{R}$

8. $\displaystyle q_{i}\in \mathbb{R}$

where $\displaystyle \neg \exists

V=(x_{v},n_{v},q_{v},s_{v})(V\notin W\wedge V\text{ satisfies 1{}-8})$

Any help solving for W would be appreciated.

Thanks,

Silly