Question

So sánh

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

Answer 1

Ta có : 

\(\frac{a}{b+c}>\frac{a}{a+b+c}\)

\(\frac{b}{c+a}>\frac{b}{a+b+c}\)

\(\frac{c}{a+b}>\frac{c}{a+b+c}\)

\(\Rightarrow\)\(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}>\frac{a}{a+b+c}+\frac{b}{a+b+c}+\frac{c}{a+b+c}\)

\(\Rightarrow\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}>\frac{a+b+c}{a+b+c}\)

\(\Rightarrow\frac{a}{c+b}+\frac{b}{a+c}+\frac{c}{a+b}>1\)

Chúc bạn học tốt !!! 

Answer 2

a/b+c > a/a+b+c           (1)

b/c+a > b/a+b+c           (2)

c/a+b > c/a+b+c           (3)

Lấy (1)+(2)+(3) ta có

a/b+c + b/c+a +c/a+b < 1

Answer 3

Ta có:

\(\frac{a}{b+c}>\frac{a}{a+b+c};\frac{b}{a+b+c}>\frac{b}{a+b+c};\frac{c}{a+b}>\frac{c}{a+b+c}\)

\(\Leftrightarrow\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}>\frac{a}{a+b+c}+\frac{b}{a+c+b}+\frac{c}{a+b+c}\)

\(\Leftrightarrow\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}>\frac{a+b+c}{a+b+c}\)

Ta thấy \(\frac{a+b+c}{a+b+c}=1\)

\(\Leftrightarrow\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}>1\)

Vậy......

Cô nàng Vân Anh cũng hỏi câu này à?? Lạ nhé!!