Question

Giải phương trình

x-a/b+c + x-b/c+a + x-c/a+b = 3

Answer 1

\(\frac{x-a}{b+c}+\frac{x-b}{c+a}+\frac{x-c}{a+b}=3\Leftrightarrow\frac{x-a}{b+c}-1+\frac{x-b}{c+a}-1+\frac{x-c}{a+b}-1=0\)

\(\Leftrightarrow\frac{x-a-b-c}{b+c}+\frac{x-b-c-a}{c+a}+\frac{x-c-a-b}{a+b}=0\)

\(\Leftrightarrow\frac{x-\left(a+b+c\right)}{b+c}+\frac{x-\left(a+b+c\right)}{c+a}+\frac{x-\left(a+b+c\right)}{a+b}=0\Rightarrow x-\left(a+b+c\right)=0\Leftrightarrow x=a+b+c\)