Question

\(Choa,b,c>0thoaman:\frac{2016c-b-a}{c}=\frac{2016b-a-c}{b}=\frac{2016a-b-c}{a}.\)

\(TnhA=\left(1+\frac{a}{b}\right)\left(1+\frac{b}{c}\right)\left(1+\frac{c}{a}\right)\)

Answer 1

+ Nếu a+b+c=0 => a+b=-c; a+c=-b; b+c=-a

A = (1 + a/b)(1 + b/c)(1 + c/a)

A = a+b/b . (b+c/c) . (c+a/a)

A = -c/b . (-a/c) . (-b/a)

A = -1

+ Nếu a+b+c khác 0

Áp dụng t/c của dãy tỉ số = nhau ta có:

2016c-b-a/c = 2016b-a-c/b = 2016a-b-c/a

= (2016c-b-a)+(2016b-a-c)+(2016a-b-c)/a+b+c

= 2015(a+b+c)/a+b+c = 2015

=> 2015c = 2016c-b-a; 2015b=2016b-a-c; 2015a = 2016a-b-c

=> c-b-a=0; b-a-c=0; a-b-c=0

=> c=a+b; b=a+c; a=b+c

A = a+b/b . (b+c/c) . (c+a/a)

A = c/b . a/c . b/a = 1