If `a ,b ,c` are in A.P., prove that the following are also in A.P. `1/(b c),1/(c a),1/(a b),` (ii) `b+c ,c+a ,a+b` (iii) `a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)` (iv) `a^2(b+c),b^2(c+a),c^2(a+b)` (v) `{(c+c)^2-a^2},{(c+a)^2-b^2},{(a+b)^2-c^2}` (vi) `1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))`

Explanation

Let ` (1)/(bc) , (1)/(ca) , (1)/(ab) ` are in A.P.
` rArr (abc)/(bc) , (abc)/(ca) , (abc) /(ab) ` are in A.P… (multiply by abc)
` rArr a , b, c` are in A.P. , which is given to be true .
Hence ` (1)/(bc) , (1)/(ca) , (1), (ab) ` are in A.P.