Question

cho a, b, c khác 0 thoả mãn  (a+b-c)/c=(b+c-a)/a=(c+a-b)/b. Tính B=(1+b/a)*(1+c/b)*(1+a/c)

Answer 1

áp dụng tính chất của DTS bằng nhau ta được:

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

\(=\frac{a+b+c}{a+b+c}=1\)

Suy ra: \(\frac{a+b-c}{c}=1\Rightarrow a+b-c=c\Rightarrow a+b=2c\)

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

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

=>\(B=\left(1+\frac{b}{a}\right)\left(1+\frac{c}{b}\right)\left(1+\frac{a}{c}\right)=\frac{a+b}{a}.\frac{b+c}{b}.\frac{c+a}{c}\)

\(=\frac{2c}{a}.\frac{2a}{b}.\frac{2b}{c}=8\)