Найди корень уравнения:

1) $x+ \frac{2}{x} =7 \frac{2}{7}$ | 1 число *7х, 2 - *7, 3 - х
7х²+14=51х
7х²-51х+14=0
D=51²-4*7*14=2601-392=2209
x₁= $\frac{51+ \sqrt{2209}}{2*7} = \frac{51+47}{14} = \frac{98}{14} = 7$
х₂= $\frac{51- \sqrt{2209}}{2*7} = \frac{51-47}{14} = \frac{4}{14} = \frac{2}{7}$

2) $y- \frac{y}{7} =5 \frac{1}{7}$ | 1 число *7
7у-у=36
6у=36
у=36:6
у=6

3) $y- \frac{1}{y} =8 \frac{8}{9}$ | 1 число *9у, 2- *9, 3- *у
9у²-9=80у
9у²-80у-9=0
D=80²-4*9*(-9)= 6400+324=6724
x₁= $\frac{80+ \sqrt{6724}}{2*9} = \frac{80+82}{18} = \frac{162}{18} =9$
х₂= $\frac{80- \sqrt{6724}}{2*9} = \frac{80-82}{18} = \frac{-2}{18} =- \frac{1}{9}$

4) $y+ \frac{3}{y} =10 \frac{3}{10}$ | 1 число *10у, 2- *10, 3- *у
10у²+30=103у
10у²-103у+30=0
D=103²-4*10*30=10609-1200=9409
х₁= $\frac{103+ \sqrt{x9409}}{2*10} = \frac{103+97}{20} = \frac{200}{20} =10$
х₂= $\frac{103- \sqrt{9409}}{2*10} = \frac{103-97}{20} = \frac{6}{20} = \frac{3}{10} =0,3$