Question

cho 3 số a, b, c thuộc R t/m \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a^{^{ }}+b+c}\)

cmr: \(\frac{1}{a^{2015}}+\frac{1}{b^{2015}}+\frac{1}{c^{2015}}=\frac{1}{a^{2015}+b^{2015}+c^{2015}}\)

mong được mọi người giúp đỡ

Answer 1

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

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

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

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

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

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

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

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

Tự làm nốt