phương trình [2^(x-1)^2]^x+1.3^x-1 có bao nhiêu nghiệm thực

* Hướng dẫn giải

Đáp án B

$$\begin{gathered} {\left[2^{{\left(\mathrm{x}-1\right)}^2}\right]}^{\mathrm{x}+1}.3^{\mathrm{x}-1}=1 \\ \iff {\left[2^{{\left(\mathrm{x}-1\right)}^2}\right]}^{\mathrm{x}+1}=3^{1-\mathrm{x}} \\ \iff {\log }_3{\left[2^{{\left(\mathrm{x}-1\right)}^2}\right]}^{\mathrm{x}+1}=1-\mathrm{x} \\ \iff (\mathrm{x}+1){(\mathrm{x}-1)}^2{\log }_{3}2+\mathrm{x}-1=0 \\ \iff (\mathrm{x}-1)\left[(\mathrm{x}+1)(\mathrm{x}-1){\log }_{3}2+1\right]=0 \\ \iff \mathrm{x}=1 \mathrm{hoặc} (\mathrm{x}+1)(\mathrm{x}-1){\log }_{3}2+1=0(*) \\ (*)\iff {\mathrm{x}}^2-1=\frac{-1}{{\log }_{3}2} \\ \iff {\mathrm{x}}^2=\frac{-1}{{\log }_{3}2}+1 \\ \mathrm{Ta} \mathrm{thấy} \frac{-1}{{\log }_{3}2}+1<0 \mathrm{nên} (*) \mathrm{vô} \mathrm{nghiệm} \\ \mathrm{KL}:\hspace{0.17em}\mathrm{PT} \mathrm{có} \mathrm{nghiệm} \mathrm{duy} \mathrm{nhất} \mathrm{x}=1 \end{gathered}$$