Solve {c}{a_{2}a_{5}=-8a^2+q^5=8/25}{y=1/3}

$$\left. \begin{array} { c } { a _ { 2 } a _ { 5 } = - 8 a ^ { 2 } + q ^ { 5 } = \frac { 8 } { 25 } } \\ { y = \frac { 1 } { 3 } } \end{array} \right.$$

Solve for a_2, a_5, a, q

$$\left\{\begin{matrix}\\a_{2}=\frac{q^{5}-8a^{2}}{a_{5}}\text{, }a_{5}\neq 0\text{, }a\in \mathrm{R}\text{, }q\in \mathrm{R}\text{, }&\text{unconditionally}\\a_{2}\in \mathrm{R}\text{, }a_{5}=0\text{, }a=-\frac{\sqrt{2}q^{\frac{5}{2}}}{4}\text{, }q\in \mathrm{R}\text{; }a_{2}\in \mathrm{R}\text{, }a_{5}=0\text{, }a=\frac{\sqrt{2}q^{\frac{5}{2}}}{4}\text{, }q\in \mathrm{R}\text{, }&q\geq 0\end{matrix}\right.$$