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The sum of the number and …

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The sum of the number and its reciprocal is 2 ×1/30.find the number

  • 1 answers

Sia ? 4 years, 9 months ago

Let the number be x and its reciprocal be {tex}{1 \over x}{/tex}

According to the question

{tex}x + {1 \over x} = 2{1 \over 30}{/tex}

{tex}\implies {x^2 +1 \over x} = {61 \over 30}{/tex}

{tex}\implies{/tex}30x2 - 61 x+30 = 0

{tex}\implies{/tex}30 x2 - 36x - 25x + 30 =0

{tex}\implies{/tex}6x ( 5x -6) - 5 (5x -6) = 0

{tex}\implies{/tex}(6x - 5) (5x - 6) = 0

Either 6x - 5 = 0 or 5x - 6 = 0

{tex}\implies x = {5 \over 6}, {6 \over 5}{/tex}
Hence, the required number is {tex}{5 \over 6} \,or \,{6 \over5}{/tex}

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