Question

Cho a,b,c là các số hưu tỉ khác 0 sao cho:
\(\frac{a+b-c}{c}\)=\(\frac{a-b+c}{b}\)=\(\frac{-a+b+c}{a}\)

Tính giá trị bằng số của 1 biểu thức:

M=\(\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}\)

Answer 1

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

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

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

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

\(\Rightarrow\)\(M=\left(\frac{a+b}{c}\right)^3=\left(\frac{a+c}{b}\right)^3=\left(\frac{b+c}{a}\right)^3\)