If `a+b+c=1`, the greatest value of `(ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a)`, isA. `(1)/(3)`B. `(1)/(2sqrt(2))`C. `(1)/(2)`D. `(1)/(4)`

If `a+b+c=1`, the greatest value of `(ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a)`

1.	If `a+b+c=1`, the greatest value of `(ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a)`, isA. `(1)/(3)`B. `(1)/(2sqrt(2))`C. `(1)/(2)`D. `(1)/(4)`
Answer» Correct Answer - C Using `A.MgeH.M.,` we have `(a+b)/(2)ge(2ab)/(a+b),(b+c)/(2)ge(2bc)/(b+c)" and "(c+a)/(2)ge(2ca)/(c+a)` `implies" "a+b+cge2((ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a))` `implies" "(1)/(2)ge(ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a)`

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