Question

Cho \(\frac{2016c-2017b}{2015}\)\(=\)\(\frac{2017a-2015c}{2016}\)\(=\)\(\frac{2015b-2016a}{2017}\)Chứng minh \(\frac{a}{2015}=\frac{b}{2016}=\frac{c}{2017}\)                                                         

Answer 1

\(\frac{2016c-2017b}{2015}=\frac{2017a-2015c}{2016}=\frac{2015b-2016a}{2017}\)

\(\Rightarrow\frac{2016c.2015-2017b.2015}{2015^2}=\frac{2017a.2016-2015c.2016}{2016^2}=\frac{2017.2015b-2017.2016a}{2017^2}\)

\(=\frac{2016c.2015-2017b.2015+2017a.2016-2015a.2016+2017.2015b-2017.2016a}{2015^2+2016^2+2017^2}=0\)

Do đó: \(2016c.2015-2017b.2015=0\Rightarrow2016c=2017b\Rightarrow\frac{b}{2016}=\frac{c}{2017}\)

\(2017a.2016-2015c.2016=0\Rightarrow2017a=2015c\Rightarrow\frac{a}{2015}=\frac{c}{2017}\)

Vậy \(\frac{a}{2015}=\frac{b}{2016}=\frac{c}{2017}\)