abc are distinct nonzero numbers such that $a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c

Question

abc are distinct nonzero numbers such that $a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c}+\frac{1}{a}\right), c\left(\frac{1}{a}+\frac{1}{b}\right)$ are in AP. Then

Professor PC Thomas Classes · Answer

$\begin{aligned} & a\left(\frac{1}{b}+\frac{1}{c}ight), b\left(\frac{1}{c}+\frac{1}{a}ight), c\left(\frac{1}{a}+\frac{1}{b}ight) \Rightarrow A \cdot P \ & a\left(\frac{1}{b}+\frac{1}{c}ight)+1, b\left(\frac{1}{c}+\frac{1}{a}ight)+1, c\left(\frac{1}{a}+\frac{1}{b}ight)+1 \Rightarrow P \ & a\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}ight) b\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}ight) c\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}ight) \Rightarrow A \cdot P \ & a, b \cdot c ightarrow A P\end{aligned}$