Question

2^(2x-3)-3*2^(x-2)+1=0

Answer 1

$displaystyle 2^{2x-3}-3*2^{x-2}+1=0 \ \ frac{2^{2x}}{8}- frac{3*2^{x} }{4}+1=0 \ \ frac{2^{2x}-6*2^{x}+8}{8}=0 \ \ 2^{2x}-6*2^{x} +8=0 \ 2^{x}=y \ y^{2}-6y+8=0 \ D=b^{2}-4ac=36-32=4 \ \ y_{1,2}= frac{-bб sqrt{D}}{2a} \ \ y_{1}=4 \y_{2}=2 \ \ 2^{x}=4 \ x=2 \ \2^{x}=2 \ x=1$

Ответ: {1; 2}