InterviewSolution
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InterviewSolution
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If `a_(i)gt0` for `i u=1, 2, 3, … ,n` and `a_(1)a_(2)…a_(n)=1,` then the minimum value of `(1+a_(1))(1+a_(2))…(1+a_(n))`, isA. `2^(n//2)`B. `2^(n)`C. `2^(2n)`D. 1 |
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Answer» Correct Answer - B Using `A.MgeG.M`, we have `(1+a_(1))gesqrt(1xxa_(1))implies1+a_(1)ge2sqrt(a_(1))` `(1+a_(2))/(2)gesqrt(1xxa_(2))implies1+a_(2)ge2sqrt(a_(2))` `vdots" "vdots" "vdots` `(1+a_(n))/(2)lesqrt(1xxa_(n))implies1+a_(n)ge2sqrt(a_(n))` `:." "(1+a_(1))(1+a_(2))...(1+a_(n))ge2^(n)sqrt(a_(1)a_(2)...a_(n))` `implies" "(1+a_(1))(1+a_(2))...(1+a_(n))ge2^(n)` |
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