Question

Решите уравнение z-2/z=4/3z-z/3

Answer 1

$\large \: \bf \: z - \frac{2}{z} = \frac{4}{3z} - \frac{z}{3} ; \\ \underbrace{z} _{3z} - \underbrace{ \frac{2}{z} } _{3} = \frac{4}{3z} - \underbrace{ \frac{z}{3} } _{z}; \\ 3 {z}^{2} -6 = 4 - {z}^{2} ; \\ 4 {z}^{2} = 10; \\ z {\tiny \: 1,2} = \pm \: \sqrt{2.5} . \\ ODZ : z \neq \: 0; \Rightarrow \: \\ \Rightarrow \: \boxed{ \bf \Huge \: \: z{ \large \: \it\: 1,2} = \pm \: \sqrt{2.5} } .$