Question

Cho a,b,c khác 0. giải phương trình \(\frac{x-b-c}{a}+\frac{x-c-a}{b}+\frac{x-a-b}{c}=3\)

Answer 1

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

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

=> x=p=(a+b+c)

Answer 2

sao lại là p

Answer 3

Ký hiệu viết cho thôi

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Answer 4

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

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

\(\left(x-a-b-c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=0\)

Cọn lại tự giải nha

Answer 5

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

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

\(\Rightarrow\left(x-a-b-c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=0\)

Với \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)=> vô số nghiệm

Với \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ne0\Rightarrow x=a+b+c\Leftrightarrow S=\left\{a+b+c\right\}\)