Question

Cho a,b,c là các số thực dương thoả mãn : a/b=b/c=c/a

Tính S= (4a-5b+2019c)/(5a-5b+2020c)

 

Answer 1

ta co: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1.\)

=> a = b = c 

\(\Rightarrow S=\frac{4a-5b+2019c}{5a-5b+2020c}=\frac{4a-5a+2019a}{5a-5a+2020c}=\frac{2018a}{2020a}=\frac{1009}{1010}\)

Answer 2

ta co: a/b=b/c=c/a =  (a+b+c)/(b+c+a) = 1

=> a/b = 1 => a = b

b/c =  1 => b = c

=> a = b = c

\(\Rightarrow S=\frac{4a-5a+2019a}{5a-5a+2020a}=\frac{2018a}{2020a}=\frac{1009}{1010}.\)

Answer 3

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

\(\text{Suy ra :}\)

\(\frac{a}{b}=1\Leftrightarrow a=b\)(1)

\(\frac{b}{c}=1\Leftrightarrow b=c\)(2)

\(\text{Từ (1) và (2) suy ra }:\): \(a=b=c\)

\(S=\frac{4a-5b+2019c}{5a-5b+2020c}=\frac{4a-5a+2019a}{5a-5a+2020a}=\frac{2018a}{2020a}=\frac{1009}{1010}\)

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