{l}{a*(1+q)=2}{a_{1}(1+q+q^2)=-6} କୁ ସମାଧାନ କରନ୍ତୁ

$$\left\{ \begin{array} { l } { a \cdot ( 1 + q ) = 2 } \\ { a _ { 1 } ( 1 + q + q ^ { 2 } ) = - 6 } \end{array} \right.$$

a, q, a_1 ପାଇଁ ସମାଧାନ କରନ୍ତୁ

$$a=\frac{2}{q+1}\text{, }q=-\frac{\sqrt{-3a_{1}^{2}-24a_{1}}}{2a_{1}}-\frac{1}{2}\text{, }a_{1}\in [-8,0)\text{; }a=\frac{2}{q+1}\text{, }q=\frac{\sqrt{-3a_{1}^{2}-24a_{1}}}{2a_{1}}-\frac{1}{2}\text{, }a_{1}\in [-8,-6)\cup (-6,0)$$