A1+a4=13 a2+a3=4 найдите a1, a2, a3, a4

[latex] \left \{ {{ a_{1} +a_{4}=13 } \atop { a_{2}+a_{3}=4 }} \right. \\ \\ \left \{ {{a_{1}+ a_{1}*q^{3}=13} \atop {a_{1}*q+a_{1}*q^{2} =4}} \right. \\ \\ \left \{ {{ a_{1}(1+q^{3})=13 } \atop {a_{1}*q(1+q)=4 }} \right. \\ \\ \frac{(1+q)(1-q+q^{2}) }{q(1+q)} = \frac{13}{4} \\ \\ \frac{1-q+q^{2} }{q} = \frac{13}{4} \\ \\ 4-4q+4 q^{2} -13q=0; \\ 4 q^{2} -17q+4=0; \\ D=289-64=225; \sqrt{D} =15. \\ \\ q_{1}= \frac{17-15}{8} = \frac{2}{8}= \frac{1}{4} ; q_{2} = \frac{17+15}{8}=[/latex]