Question

СРОЧНО ПОМОГИТЕ!!!!Найдите знаменатель геометрической прогрессии система b3b7=256 b5+b7=80

Answer 1

$\left \{ {{b_{3}*b_{7}=256} \atop {b_{5}+b_{7}=80}} \right.\\\\\left \{ {{b_{1}*q^{2}*b_{1} *q^{6}=256} \atop {b_{1}q^{4}+b_{1}q^{6}=80}} \right. \\\\\left \{ {{b_{1}^{2}*q^{8} =256} \atop {b_{1}q^{4}(1+q^{2})=80}} \right.\\\\1)\left \{ {{b_{1}q^{4}=16} \atop {16(1+q^{2})=80}} \right.\\\\\left \{ {{b_{1}q^{4}=16\atop {q^{2}+1-5=0 }} \right.$

$\left \{ {{b_{1}q^{4}=16} \atop {q^{2}=4 }} \right.\\\\\left \{ {{q_{1}=-2 } \atop {b_{1}=1 }} \right. \\\\\left \{ {{q_{2}=2 } \atop {b_{1}=1 }} \right.$

$2)\left \{ {{b_{1}q^{4}=-16} \atop {-16(1+q{2})=80 }} \right.\\\\\left \{ {{b_{1}q^{4}=-16} \atop {q^{2}+1+5=0 }} \right.\\\\q^{2}=-6\Rightarrow q\in\oslash \\\\Otvet:\boxed{ q_{1} =-2;q_{2}=2}$