Question

[Nguyễn Thị Ngọc Mai]

Cho a,b,c thỏa mãn 1/a+1/b+1/c=1/a+b+c . CMR: a+b=0 hoặc  b+c=0 hoặc c+a=0

Answer 1

[Nguyễn Nguyệt Anh]

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

<=>\(\frac{a+b}{ab}=\frac{-\left(a+b\right)}{c\left(a+b+c\right)}\)

<=>c(a+b)(a+b+c)=-ab(a+b)

<=>(a+b)(ac+bc+c²)+ab(a+b)=0

<=>(a+b)(ac+bc+ab+c²)=0

<=>(a+b)(a+c)(c+b)=0

       a+b=0

<=> b+c=o

       c+a=0