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Question

If $x subscript i end subscript greater than 0 comma i equals 12 comma horizontal ellipsis comma 50$ and $x subscript 1 end subscript plus x subscript 2 end subscript plus midline horizontal ellipsis plus x subscript 50 end subscript equals 50$ , then the minimum value of $fraction numerator 1 over denominator x subscript 1 end subscript end fraction plus fraction numerator 1 over denominator x subscript 2 end subscript end fraction plus midline horizontal ellipsis plus fraction numerator 1 over denominator x subscript 50 end subscript end fraction$ equals

50
$(50)^{2}$
$(50)^{3}$
$(50)^{4}$

The correct answer is: 50

$text We have end text open parentheses x subscript 1 end subscript plus x subscript 2 end subscript plus x subscript 3 end subscript plus midline horizontal ellipsis plus x subscript 50 end subscript close parentheses open parentheses fraction numerator 1 over denominator x subscript 1 end subscript end fraction plus fraction numerator 1 over denominator x subscript 2 end subscript end fraction plus midline horizontal ellipsis fraction numerator 1 over denominator x subscript 50 end subscript end fraction close parentheses greater or equal than left parenthesis 50 right parenthesis to the power of 2 end exponent$
$rightwards double arrow open parentheses fraction numerator 1 over denominator x subscript 1 end subscript end fraction plus fraction numerator 1 over denominator x subscript 2 end subscript end fraction plus midline horizontal ellipsis fraction numerator 1 over denominator x subscript 50 end subscript end fraction close parentheses greater or equal than left parenthesis 50 right parenthesis$

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parallel

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