11002, ........,a,,are positive rea...
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11002, ........,a,,are positive real numbers whose product is a fixed number c, then the minimum value of a tapt...... tan-1 + 2a, is (A) n(2c)/ (B) (n + 1)c1in (C) 2nclln (D) (n + 1)(2c)1/n

JEE/Engineering Exams
Maths
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anen that ( a_{1} ; a_{2}, a_{3} ldots ) an be positive real numbers such that ( a, a, ldots . a_{n}=c ) 0 we know that A.M ( geq ) G.M ( Rightarrow frac{a_{1}+a_{2}+ldots+a_{n-1}+2 a_{n}}{n} geqleft(a_{1} a_{2} cdots a_{n-1}left(2 a_{n}right)right)^{1 / n} ) ( Rightarrow a_{1}+a_{2}+ldots+a_{n-1}+2 a_{n} geq n(2 c)^{1 / 2} ) feom 0 so, the minimum dalup of ( a_{1}+a_{2}+ldots+a_{n-1}+2 a_{n} ) is ( n(2 c)^{1 / n} )
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