Question

Cho a,b,c khác 0 thỏa mãn.

a+b-c/c = b+c-a/a = c+a-b/b

Tính P = ( 1+ b/a) . ( 1+a/c) . (1+c/b)

Answer 1

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

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

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

Xét \(a+b+c\ne0\Rightarrow a=b=c\). Khi đó \(P=2\cdot2\cdot2=8\)

Xét \(a+b+c=0\Rightarrow\)\(\left\{\begin{matrix}a+b=-c\\a+c=-b\\b+c=-a\end{matrix}\right.\)

Khi đó \(P=\frac{a+b}{a}\cdot\frac{a+c}{c}\cdot\frac{b+c}{b}=\frac{-c}{a}\cdot\frac{-b}{c}\cdot\frac{-a}{b}=-1\)