if a+b+c=6 and 1/a+1/b+1/c=3/2 , then find a/b+a/c+b/a+b/c+c/a+c/b ?
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->a+b+c=6…………..(1)
->1/a+1/b+1/c=3/2…………(2)
->a/b+a/c+b/c+b/a+c/a+c/b=?
=a/b+c/b+a/c+b/c+b/a+c/a
=(a+c)/b+(a+b)/c+(b+c)/a
On putting a+c=6-b , a+b=6-c and b+c=6-a from eq.(1).
=(6-b)/b+(6-c)/c+(6-a)/a
=6/b - 1 +6/c - 1 + 6/a -1
=6(1/b+1/c+1/a) -3
On putting 1/a+1/b+1/c=3/2 from eq.(2).
= 6×3/2 - 3
= 9 -3
= 6 ,Answer.
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