Cho \(\dfrac{a}{b} = \dfrac{b}{c} = \dfrac{c}{a};\,a + b + c \ne 0\) và \(a = 2018\). Tính \(b,c\).

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{{x + y}}{{a + b}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{{x.y}}{{a.b}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{{x.y}}{{a + b}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{{x - y}}{{a + b}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c} = \dfrac{{x + y + z}}{{a + b + c}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c} = \dfrac{{x - y - z}}{{a - b - c}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c} = \dfrac{{x - y + z}}{{a - b + c}}\)

\(\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c} = \dfrac{{x + y - z}}{{a - b + c}}\)

\(x =  - 20;y =  - 12\)

\(x =  - 12;y = 20\)      

\(x =  - 12;y =  - 20\)  

\(x = 12;y =  - 20\)

\(27;\,33\)

\(33;27\)

\(27;44\)

\(27;34\)

\(y = 4;x = 7\)

\(x = 32;y = 56\)

\(x = 56;y = 32\)

\(x = 4;y = 7\)

\(6;\,12;14;\,18\)

\(18;14;10;6\) 

\(6;14;10;18\)

\(6;10;14;18\)

\(27\)

\( - 27\)

\( - 18\)

\( - 45\)