Question

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

Answer 1

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

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

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