Question

under root x/ under root x-1 + under root x-1/ under root x = 3​

Answer 1

Answer:

$\sqrt{ \frac{x}{x - 1} } + \sqrt{ \frac{x - 1}{x} } = 3$

$\sqrt{ \frac{ {x}^{2} + (x - 1) {}^{2} }{x(x - 1)} } = 3$

squaring both sides

${x}^{2} + {x}^{2} - 2x + 1 = 9 {x}^{2} - 9x$

$7 {x}^{2} - 7x - 1 = 0$

$x = \frac{7 + \sqrt{49 + 28} }{14} = \frac{7 + \sqrt{77} }{14}$