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

Posted by John Dungdung 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

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

According to the question

$x + {1 \over x} = 2{1 \over 30}$

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

$\implies$ 30x² - 61 x+30 = 0

$\implies$ 30 x² - 36x - 25x + 30 =0

$\implies$ 6x ( 5x -6) - 5 (5x -6) = 0

$\implies$ (6x - 5) (5x - 6) = 0

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

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

0Thank You

ANSWER

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