Question

Реши уравнение 2⋅2^2x+5⋅2^x−3=0.

Answer 1

$2*2^{2x}+5*2^{x}-3=0\\\\2^{x}=m,m>0\\\\2m^{2}+5m-3=0\\\\D=5^{2}-4*2*(-3)=25+24=49=7^{2}\\\\m_{1}=\frac{-5+7}{4}=\frac{1}{2} \\\\m_{2}=\frac{-5-7}{4}=-3<0-neyd\\\\2^{x} =\frac{1}{2}\\\\2^{x}=2^{-1} \\\\x=-1\\\\Otvet:\boxed{-1}$