Question

Решите неравенство: $2^{2x-1} -3* 2^{x-1} +1 textless 0$

Answer 1

1/2*2^2x-3/2*2^x+1<0
2^2x-3*2^x+2<0
2^x=a
a²-3a+2<0
a1+a2=3 U a1*a2=2⇒a1=1 U a2=2
1<a<2⇒1<2^x<2⇒0<x<1
x∈(0;1)