Ta có:
\(\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)^2=\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\right)\)
\(=\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{2\left(a+b+c\right)}{abc}=\frac{1}{a^2}+\frac{1}{b^2}+\frac{2c}{abc}\)
\(=\frac{1}{a^2}+\frac{1}{b^2}+\frac{2}{ab}+\frac{1}{c^2}=\left(\frac{1}{a}+\frac{1}{b}\right)^2+\frac{1}{c^2}\)
Bạn ghi nhầm đề thì phải