Question

Помогите пожалуйста решить уравнение!!!!

Answer 1

$frac{sqrt{x}+1}{sqrt{x}-1}-frac{sqrt{x}-1}{sqrt{x}+1}=2sqrt{x^3}\ x neq +-1\\ frac{sqrt{x}+1}{sqrt{x}-1} - frac{sqrt{x}-1}{sqrt{x}+1} = 2xsqrt{x}\\ sqrt{x}+1=t(sqrt{x}-1)\ \ tsqrt{x}-sqrt{x}=t+1\\ sqrt{x}=frac{t+1}{t-1}\\ t-frac{1}{t}=2*frac{(t+1)^3}{(t-1)^3}\\ (t^2-1)(t-1)^3=2t(t+1)^3\\ (t+1)(t-1)^4=2t(t+1)^3\\ (t+1)((t-1)^4-2t(t+1)^2)=0\ t=-1\ t=3-sqrt{8}; t=sqrt{8}-3$             
 $t=-1\ t=3-sqrt{8}\ t=sqrt{8}+3\\ frac{sqrt{x}+1}{sqrt{x}-1} = -1\ sqrt{x}+1=1-sqrt{x}\ x=0\\ sqrt{x}+1 = (sqrt{8}+3)sqrt{x}-sqrt{8}-3\\ x=2$ 
Ответ $x=0;2$