Question

[Nguyễn Thu Hiền]

Cho cac so a,b,c,d thoa man: \(\frac{a}{b+c+d}=\frac{b}{c+d+a}=\frac{c}{d+a+b}=\)

\(\frac{d}{a+b+c}\). Tinh gia tri bieu thuc: 

P=\(\frac{a+b}{c+d}=\frac{b+c}{d+a}=\frac{c+d}{b+a}=\frac{d+a}{b+c}\)

Answer 1

[Phùng Minh Quân]

Ta có :

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

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

\(\Leftrightarrow\)\(\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{c+d+a}=\frac{a+b+c+d}{d+a+b}=\frac{a+b+c+d}{a+b+c}\)

Ta thấy các tử bằng nhau suy ra các mẫu bằng nhau 

\(\Rightarrow\)\(b+c+d=c+d+a=d+a+b=a+b+c\)

\(\Rightarrow\)\(a=b=c=d\)

\(\Rightarrow\)\(\frac{a+b}{c+d}+\frac{b+c}{d+a}+\frac{c+d}{b+a}+\frac{d+a}{b+c}=1+1+1+1=4\)

Đề bị nhầm đúng ko bạn ^^