Question

CÁC BẠN HỘ MÌNH VỚI

cmr nêu ạ,b,c thỏa mãn : 1/a+1/b+1/c=1/a+b+c thì 2 trong 3 số fải đối nhau 

 

Answer 1

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

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

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

\(\Leftrightarrow\frac{a+b}{ab}=\frac{-\left(a+b\right)}{ac+bc+c^2}\)

\(\Leftrightarrow\left(a+b\right)\left(ac+bc+c^2\right)=-\left(a+b\right)ab\)

\(\Leftrightarrow\left(a+b\right)\left(ac+bc+c^2\right)+\left(a+b\right)ab=0\)

\(\Leftrightarrow\left(a+b\right)\left(ac+bc+c^2+ab\right)=0\)

\(\Leftrightarrow\left(a+b\right)\left(a+c\right)\left(b+c\right)=0\)

=> a = - b hoặc b = - c hoặc c = - a (đpcm)