Question

Найдите первый член убывающей арифметической прогрессии (аn),если а7+а2=5,а5*а4=-36

Answer 1

$\left \{ {{a_7+a_2=5} \atop {a_5*a_4=-36}} \right. \\\\ \left \{ {{a_1+6d+a_1+d=5} \atop {(a_1+4d)(a_1+3d)=-36}} \right.\\\\ \left \{ {{2a_1+7d=5} \atop {(a_1+4d)(a_1+3d)=-36}} \right. \\\\ \left \{ {{2a_1=5-7d} \atop {(a_1+4d)(a_1+3d)=-36}} \right.\\\\ \left \{ {{a_1=2,5-3,5d} \atop {(2,5-3,5d+4d)(2,5-3,5d+3d)=-36}} \right.\\\\ \left \{ {{a_1=2,5-3,5d} \atop {(2,5+0,5d)(2,5-0,5d)=-36}} \right. \\\\ \left \{ {{a_1=2,5-3,5d} \atop {(2,5)^2-(0,5d)^2=-36}} \right.$
$6,25-0,25d^2=-36\\0,25d^2=6,25+36\\0,25d^2=42,25\\d^2=42,25:0,25\\d^2=169\\d= \sqrt{169}\\d=13\\a_1=2,5-3,5*13=2,5-45,5=-43$

Ответ: а₁=-43