State true or false:
A number added to its reciprocal gives result as $4.25$ then the number is $4 o r \frac{1}{4}$ .

True

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False

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Solution

The correct option is A True
Let the number be $x$
Then, $x + \frac{1}{x} = 4.25$

$x^{2} + 1 = 4.25 x$
$x^{2} - 4.25 x + 1 = 0$
$x^{2} - 4 x - 0.25 x + 1 = 0$
$(x - 4) (x - \frac{1}{4})$
$∴ x = 4, \frac{1}{4}$

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