Question

cho day ti so bang nhau

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

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

Answer 1

\(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=d\)

\(\Rightarrow\frac{2a+b+c+d}{a}-1=\frac{a+2b+c+d}{b}-1=\frac{a+b+2c+d}{c}-1=\frac{a+b+c+2d}{d}-1\).

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

Nếu a+b+c+d\(\ne\)0=>a=b=c=d

=>M=a+b/c+d + b+c/d+a + c+d/a+b + a+d/b+c=1+1+1+1=4

Nếu a+b+c+d=0=>a+b=-(c+d)

b+c=-(a+d)

=>M=a+b/c+d + b+c/d+a + c+d/a+b + d+a/b+c =-1+(-1)+(-1)+(-1)=-4