Question

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

4 . ( a - b ) . ( b - c ) = ( c - a ) ²

Answer 1

\(\frac{a}{2015}=\frac{b}{2016}\)

=>a=\(\frac{2015}{2016}b\)

\(\frac{b}{2016}=\frac{c}{2017}\)

=>c=\(\frac{2017}{2016}b\)

\(4.\left(a-b\right).\left(b-c\right)=4.\left(\frac{2015}{2016}b-b\right).\left(b-\frac{2017}{2016}b\right)=4.\frac{-1}{2016}b.\frac{-1}{2016}b=\frac{1}{1016064}b^2\)

\(\left(c-a\right)^2=\left(\frac{2017}{2016}b-\frac{2015}{2016}b\right)^2=\left(\frac{1}{1008}b\right)^2=\frac{1}{1016064}b^2\)

=>ĐPCM