Question

Tìm a,b,c biết \(\frac{a}{2014}=\frac{b}{3}=\frac{c}{2}\)và 2015b - 2016c - a = -1

Answer 1

Ta co : \(\frac{a}{2014}=\frac{b}{3}=\frac{c}{2}\Rightarrow\frac{a}{2014}=\frac{2015b}{6045}=\frac{2016c}{4032}\) va 2015b-2016b-a=-1

Ap dung tinh chat day ti so bang nhau : 

\(\frac{2015b}{6045}=\frac{2016c}{4032}=\frac{a}{2014}=\frac{2015b-2016b-a}{6045-4032-2014}=-\frac{1}{-1}=1\)

Suy ra : \(\frac{2015b}{6045}=1\Rightarrow b=1.6045:2015=3\)

\(\frac{2016c}{4032}=1\Rightarrow c=1.4032:2016=2\)

\(\frac{a}{2014}=1\Rightarrow a=1.2014=2014\)

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