Question

Помогите с уравнением:

Answer 1

$3\cdot 2^{\frac{x-1}{\sqrt{x}+1}}-8\cdot 2^{\frac{\sqrt{x}-1}{2}}+4=0\\\\3\cdot 2^{\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}+1}}-8\cdot 2^{\frac{\sqrt{x}-1}{2}}+4=0\; ,\; \; ODZ:\; x \geq 0\\\\3\cdot 2^{\frac{\sqrt{x}-1}{1}}-8\cdot 2^{\frac{\sqrt{x}-1}{2}}+4=0\\\\t=2^{\frac{\sqrt{x}-1}{2}}\; ,\; \; 3t^2-8t+4=0\\\\t_1=\frac{2}{3},\; t_2=2\\\\2^{\frac{\sqrt{x}-1}{2}}=2,\; \frac{\sqrt{x}-1}{2}=1,\; \sqrt{x}-1=2,\; \sqrt{x}=3,\; x=9\\\\2^{\frac{\sqrt{x}-1}{2}}=\frac{2}{3},\sqrt{x}-1=log_2{\frac{2}{3}},$

$\sqrt{x}=1+log_2\frac{2}{3},\; \; x=(1+log_2\frac{2}{3})^2$