If b + c, c + a, a + b are in H.P., then frac | vedclass

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Question

(a) Let $\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}$ are in $A.P.$

Add $1$ to each term, we get

$\frac{{a + b + c}}{{b + c}},\frac{{b

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$A.P.$

Vedclass · Answer

(a) Let $\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}$ are in $A.P.$

Add $1$ to each term, we get

$\frac{{a + b + c}}{{b + c}},\frac{{b + c + a}}{{c + a}},\frac{{c + a + b}}{{a + b}}$ are in $A.P.$

Divide each term by $(a + b + c),$

$\frac{1}{{b + c}},\frac{1}{{c + a}},\frac{1}{{a + b}}$ are in $A.P.$

Hence $b + c,\,\,c + a,\,\,a + b$ are in $H.P.$

which is given in question

Therefore, $\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}$ are in $A. P.$

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

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