Question

co 2a+b+c+d/a =  a+2b+c+d/b = a+b+2c+d/c = a+b+c+2d/d

tinh M= a+b/c+d + b+c/d+a + c+d/a+b + d+a/b+c

Answer 1

bn lik e bai mjh dc ko 

Answer 2

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

\(\Leftrightarrow\)a+a+b+c+d/a=a+b+b+c+d/b=a+b+c+c+d/c=a+b+c+d+d/d  

\(\Leftrightarrow\)a+b+c+d/a+1=a+b+c+d/b+1=a+b+c+d/c+1=a+b+c+d/d+1  

\(\Leftrightarrow\)a+b+c+d/a=a+b+c+d/b=a+b+c+d/c=a+b+c+d/d  

Dến đây ta xét 2 TH:  

a+b+c+d≠0  

a+b+c+d=0

Answer 3

Ta có: (2a+b+c+d/a)-1=(a+2b+c+d/b)-1=(a+b+2c+d/d)-1=(a+b+c+2d/d)-1

=>a+b+c+d/a=a+c+b+d/b=a+b+c+d/c=a+b+c+d/d

=>a=b=c=d         (1)

Ta lại có: a+b+c+d/a=a+b+c+d/b=a+b+c+d/c=a+b+c+d/d

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

=4(a+b+c+d)/a+b+c+d=4          (2)

Từ (1) và (2) => a=b=c=d=1

=> M=1+1/1+1 + 1+1+/1+1 + 1+1/1+1 + 1+1/1+1

=4