Question

A number is greater than twice its reciprocal by 31/4. Find the number

Answer 1

pardon the handwriting,hope it helps

Answer 2

Answer:

The number will be 8.

Step-by-step explanation:

Let's consider that the number is x then  its reciprocal can be given by $\dfrac{1}{x}$.

Now, according to question

   $x\ -\ \dfrac{2}{x}\ =\ \dfrac{31}{4}$

$=>\ \dfrac{x^2-2}{x}\ =\ \dfrac{31}{4}$

$=>\ x^2\ -\ 2\ =\ \dfrac{31x}{4}$

$=>\ 4x^2-\ 8\ =\ 31x$

$=>\4x^2\ -\ 31x\ -\ 8\ =\ 0$

$=>\ 4x^2\ -\ 32x\ +\ x\ -\ 8\ =\ 0$

$=>\ 4x(x\ -\ 8)\ +\ 1(x\ -\ 8)\ =\ 0$

$=>\ (4x+1)(x-8)\ =\ 0$

$=>\ x\ =\ \dfrac{-1}{4}, 8$

If we consider only positive number than the answer will be 8.