Решете abc=1text{provethat}:1/1+a+b^-1+1/1+b+c^-1+1/1+c+a^-1=1

$$a b c = 1 \text { prove that } : \frac { 1 } { 1 + a + b ^ { - 1 } } + \frac { 1 } { 1 + b + c ^ { - 1 } } + \frac { 1 } { 1 + c + a ^ { - 1 } } = 1$$

Решаване за a, b, c (complex solution)

$$a=-\frac{1}{b}\text{, }b\neq 0\text{, }c=-1$$

$$a=\frac{1}{bc}\text{, }b=-\frac{1}{2}-\frac{1}{2c}\text{, }c\in \mathrm{C}\setminus -1,0$$

Решаване за a, b, c

$$a=-\frac{1}{b}\text{, }b\neq 0\text{, }c=-1$$

$$a=\frac{1}{bc}\text{, }b=-\frac{1}{2}-\frac{1}{2c}\text{, }c\in \mathrm{R}\setminus -1,0$$