Question

Mọi Người giải hộ mình với!!!

Answer 1

Trường hợp 1: \(a+b+c+d=0\Leftrightarrow\left\{{}\begin{matrix}a+b=-c-d\\b+c=-d-a\\c+a=-b-d\\a+d=-b-c\end{matrix}\right.\)

\(\Leftrightarrow A=-1-1-1-1=-4\)

Trường hợp 2: \(a+b+c+d\ne0\)

\(\dfrac{2a+b+c+d}{a}=\dfrac{a+2b+c+d}{b}=\dfrac{a+b+2c+d}{c}=\dfrac{a+b+c+2d}{d}=\dfrac{4\left(a+b+c+d\right)}{a+b+c+d}=4\\ \Leftrightarrow\left\{{}\begin{matrix}2a+b+c+d=4a\\a+2b+c+d=4b\\a+b+2c+d=4c\\a+b+c+2d=4d\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a+b+c+d=3a\\a+b+c+d=3b\\a+b+c+d=3c\\a+b+c+d=3d\end{matrix}\right.\\ \Leftrightarrow a=b=c=d\\ \Leftrightarrow A=1+1+1+1=4\)

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