Ta có :\(\frac{a}{b+c+d}+\frac{b}{c+d+a}+\frac{c}{d+a+b}+\frac{d}{a+b+c}>\frac{a}{a+b+c+d}+\frac{b}{a+b+c+d}+\frac{c}{a+b+c+d}+\frac{d}{a+b+c+d}=\frac{a+b+c+d}{a+b+c+d}=1\)và \(\frac{a}{b+c+d}+\frac{b}{c+d+a}+\frac{c}{d+a+b}+\frac{d}{a+b+c}<\frac{2a}{a+b+c+d}+\frac{2b}{a+b+c+d}+\frac{2c}{a+b+c+d}+\frac{2d}{a+b+c+d}=\frac{2\left(a+b+c+d\right)}{a+b+c+d}=2\)

Đặt A=a/b+c+d + b/c+d+a +c/d+a+b +d/a+b+c

     4+A=a/b+c+d +1  + b/c+d+a  +1 + c/d+a+b  +1  + d/a+b+c  +1

     4+A=2a/a+b+c+d  +  2b/a+b+c+d  +  2c/a+b+c+d  +2d/a+b+c+d

     4+A=2a+2b+2c+2d/a+b+c+d

     4+A=2(a+b+c+d) /a+b+c+d

     4+A=2

       A=2-4= -2

=) A<1<2

a/b+c>a/a+b+c

b/c+a>b/a+b+c

c/a+b>c/a+b+c

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

==>biểu thức này >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 !!! 

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

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!!

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

Đáp số là M > 1. Bạn cần cách giải không ?

Co minh biet ket qua roi ban HiHI

mk chi cac bạn tuyet chieu;

nhung bai toan dang nay mk thuong lay so cu the nhu 1;2;3 .... thay vao se doan dc kq vi violympic thoi gian thi co hạn

cac ban co dong y k

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