Сумма третьего и пятого члена арифметической прогрессии равна 16, а произведение шестого и первого члена равно 64. Найдите разность и первый член данной прогрессии.

[latex]a_1+a_5=16[/latex] [latex]a_1*a_6=64[/latex] [latex]a_1-[/latex] ? [latex]d-[/latex] ? [latex] \left \{ {{a_3+a_5=16} \atop {a_1*a_6=64}} \right. [/latex] [latex] \left \{ {{a_1+2d+a_1+4d=16} \atop {a_1*(a_1+5d)=64}} \right. [/latex] [latex] \left \{ {{2a_1+6d=16} \atop {a^2_1+5a_1*d=64}} \right. [/latex] [latex] \left \{ {{a_1+3d=8} \atop {a^2_1+5a_1*d=64}} \right. [/latex] [latex] \left \{ {{a_1=8-3d} \atop {(8-3d)^2+5d(8-3d)=64}} \right. [/latex] [latex] \left \{ {{a_1=8-3d} \atop {64-48d+9d^2+40d-15d^2=64}} \right. [/latex] [latex] \left \{ {{a_1=8-3d} \atop {-8d-6d^2=0}} \right. [/latex] [latex] \left \{ {{a_1=8-3d} \atop {4d+3d^2=0}} \right. [/latex] [latex]4d+3d^2=0[/latex] [latex]d(4+3d)=0[/latex] [latex]d=0[/latex]       или  [latex]d=- \frac{4}{3} [/latex]     [latex] \left \{ {{d=0} \atop {a_1=8-3*0}} \right. [/latex]     или       [latex] \left \{ {{d=- \frac{4}{3} } \atop {a_1=8-3*(- \frac{4}{3}) }} \right. [/latex] [latex] \left \{ {{d=0} \atop {a_1=8}} \right. [/latex]       или        [latex] \left \{ {{d=- 1\frac{1}{3} } \atop {a_1=12 }} \right. [/latex]