Ta có:\(\frac{a}{b+c+d}=\frac{b}{c+d+a}=\frac{c}{a+b+d}=\frac{d}{a+b+c}\)
\(\Rightarrow\frac{b+c+d}{a}=\frac{c+d+a}{b}=\frac{a+b+d}{c}=\frac{a+b+c}{d}\)
\(\Rightarrow\frac{b+c+d}{a}+1=\frac{c+d+a}{b}+1=\frac{a+b+d}{c}+1=\frac{a+b+c}{d}+1\)
\(\Rightarrow\frac{a+b+c+d}{a}=\frac{a+b+c+d}{b}=\frac{a+b+c+d}{c}=\frac{a+b+c+d}{d}\)=\(\frac{a+b+c+d+a+b+c+d+a+b+c+d+a+b+c+d}{a+b+c+d}=4\)(T/C)
Xét a+b+c+d=0
\(\Rightarrow a+c=-\left(b+d\right),a+b=-\left(c+d\right),b+c=-\left(a+d\right)\)
\(\Rightarrow M=-1+-1+-1+-1=-4\)
Xét \(a+b+c+d\ne0\Rightarrow a=b=c=d\)
\(\Rightarrow M=1+1+1+1=4\)
Vậy M=-4 hoặc M=4
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