If a , b , c are in H.P., then a b + c , b c + a , c a + b will be in

Question

If $a, b, c$ are in H.P., then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ will be in

Smart Achievers · Accepted Answer

(3)

$Since, a, b, c are in H.P.$

$\Rightarrow$ $\frac{1}{a}, \frac{1}{b}, \frac{1}{c} are in A.P.$

$\Rightarrow$ $\frac{a + b + c}{a}, \frac{a + b + c}{b}, \frac{a + b + c}{c} are in A.P.$

$\Rightarrow$ $1 + \frac{b + c}{a}, 1 + \frac{a + c}{b}, 1 + \frac{a + b}{c} are in A.P.$

$\Rightarrow$ $\frac{b + c}{a}, \frac{a + c}{b}, \frac{a + b}{c} are in A.P.$

$\Rightarrow$ $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b} are in H.P.$

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