Question

Решить уравнения

1)$sqrt{ frac{2x}{ x^{2} -1} } - frac{2}{ sqrt{x+1} } =0$

2)$10x- sqrt{2x+1}=1$

Answer 1

$1)\sqrt{frac{2x}{x^2-1}}-frac{2}{sqrt{x+1}}=0\ frac{sqrt{2x}}{sqrt{(x-1)(x+1)}}-frac{2}{sqrt{x+1}}=0\ frac{sqrt{2x}-2sqrt{x-1}}{sqrt{x^2-1}}=0\ sqrt{2x}-2sqrt{x-1}=0\ sqrt{2x}=2sqrt{x-1}\ 2x=4(x-1)\ 2x=4x-4\ 2x=4\ x=2\ 2)\10x-sqrt{2x+1}=1\ sqrt{2x+1}=10x-1\ 2x+1=100x^2-20x+1\ 100x^2-22x=0\ x(100x-22)=0\ x=0\ x=frac{11}{50}$
Ответ $2;frac{11}{50}$