Question

1 a) CMR : Nếu \(\frac{a+2016}{a-2016}=\frac{b+2015}{b-2015}\)

Thì \(\frac{a}{2016}=\frac{b}{2015}\)

Answer 1

ta có : \(\frac{a+2016}{a-2016}=\frac{b+2015}{b-2015}\)

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

=> Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:

\(\frac{a+2016}{b+2015}=\frac{a-2016}{b-2015}=\frac{a+2016+a-2016}{b+2015+b-2015}=\frac{2a}{2b}=\frac{a}{b}\)

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

=> b(a+2016)=a(b+2015)

=>ba+b.2016= ab+a.2015

=>b.2016=a.2015 ( Rút gọn 2 vế với ab)

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

Answer 2

Nếu: \(\frac{a+2016}{a-2016}\)= \(\frac{b+2015}{b-2015}\)

(a + 2016).(b - 2015) = (b + 2015).(a - 2016)

a.b - 2015.a + 2016.b - 2015.2016 = b.a - 2016.b + 2015.a - 2015.2016

2a.2015 = 2b.2016

a.2015 = b.2016 

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