Question

solve this I'm finding it very difficult

Answer 1

Hi!

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Given :

a , b and c are in A.P.

To Prove :

$\frac{a(b+c)}{bc} , \frac{b(c + a )}{ca} , \frac{c(a + b)}{ab}$

Proof :

$\frac{a(b+c)}{bc} , \frac{b(c + a )}{ca} , \frac{c(a + b)}{ab}$

On Adding 1 ,We get

$\frac{a(b+c)}{bc} + 1 ,\frac{b(c + a )}{ca} + 1 ,\frac{c(a + b)}{ab} + 1$

$\frac{(ab + bc+ ac )}{bc} , \frac{(ab + bc + ac) }{ca} , \frac{(ab + bc + ac)}{ab}$

On Dividing by (ab + bc + ac )

$\frac{1}{bc} , \frac{1}{ca} , \frac{1}{ab}$

Multiply by abc

a , b , c

Hence , $\frac{a(b+c)}{bc} , \frac{b(c + a )}{ca} , \frac{c(a + b)}{ab}$ are in A.P.

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Thanks !!