Question

Решите уравнение 2^2x+1 +7*2^x =4

Answer 1

$2^{2x+1}+7cdot2^x=4\2cdot2^{2x}+7cdot2^x-4=0\2^x=t,;2^{2x}=t^2,;t>0\2t^2+7t-4=0\D=49-4cdot2cdot(-4)=49+32=81\t_{1,2}=frac{-7pm9}4\t_1=-4;-;He;nogx.\t_2=frac12\\2^x=frac12\2^x=2^{-1}\x=-1$