Question

the difference between a number and its reciprocal is 5
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Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let the first number be x

another number be 1/x

Now,the difference of number and it's reciprocal is 5

According to the question:

$\sf = > x - \dfrac{1}{x} = 5$

$\sf \longmapsto \dfrac{ {x}^{2} - 1 }{x} = 5$

$\sf \longmapsto {x}^{2} - 5x - 1 = 0$

$\sf x = \dfrac{ - b \pm \sqrt{ {b }^{2} - 4ac } }{2a}$

$\sf \longmapsto \: x = \dfrac{ - ( - 5) \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 1)} }{2}$

$\sf \longmapsto \: x = \dfrac{5 \pm \sqrt{25 + 4} }{2}$

$\sf \longmapsto \: x = \dfrac{5 \pm \sqrt{29} }{2}$

there are two values of x one is positive and another is -ve.

Another number is 1/x

$\sf\longmapsto \dfrac{ \dfrac{1}{5 \pm \sqrt{29} } }{2} = \dfrac{2}{5 \pm \sqrt{29} }$