If a, b and c are positive real numbers such that `aleblec,` then `(a^(2)+b^(2)+c^(2))/(a+b+c)` lies in the interval

Options

A. `((a^(2))/(c),(c^(2))/(a))`
B. `((a)/(c^(2)),(c)/(a^(2)))`
C. `((c^(2))/(a),(a^(2))/(c))`
D. `((b^(2))/(c),(c^(2))/(b))`

Answer

A

Explanation

We have,
`altbltcimplies3alta+b+clt3cimplies(1)/(3c)lt(1)/(a+b+c)lt(1)/(3a)" "...(i)`
Again,
`altbltcimpliesa^(2)ltb^(2)ltc^(2)implies3a^(2)lta^(2)+b^(2)+c^(2)lt3c^(2)" "...(ii)`
From (i) and (ii), we get
`(a^(2))/(c)lt(a^(2)+b^(2)+c^(2))/(a+b+c)lt(c^(2))/(a)implies(a^(2)+b^(2)+c^(2))/(a+b+c)in((a^(2))/(c),(c^(2))/(a))`