Question

A number is greater than twice its reciprocal by 49/5. What is the number?

Answer 1

$\sf \: Answer \:$ :

Let the number be p.

Given that,

It's greater than twice reciprocal by 49/5.

Mathematically,

$p - \frac{49}{5} = 2 \times \frac{1}{p}$

p - 2/p = 49/5

5 (p² - 2) = 49 p

5p² - 49p - 10 = 0

5p² - 50p + p - 10 = 0

5p ( p - 10) + 1 ( p - 10) = 0

( 5p + 1) ( p - 10) = 0

5p + 1 = 0 or p - 10 = 0

5p = - 1 or p = 10

p = - 1/5 or 10

$\sf \: Required \: number \: is - 1/5 \: or \: 10$