Question 1102520
if x is the number, then the reciprocal of x is 1/x.
2 times the reciprocal of x is 2/x.


x + 2/x = 33/4
multiply both sides of this equation by 4x to get 4x^2 + 8 = 33x


subtract 33x from both sides of this equation and re-order the terms in descending order of degree to get 4x^2 - 33x + 8 = 0


factor this quadratic equation to get(4x-1) * (x-8) = 0
solve for x to get x = 1/4 or x = 8


when x = 1/4, the reciprocal of x is equal to 4 and 2 times the reciprocal of x is equal to 8.
x + 2/x becomes 1/4 + 8 which becomes 1/4 + 32/4 which is equal to 33/4.


when x = 8, the reciprocal of x is equal to 1/8 and 2 times the reciprocal of x is equal to 2/8 which is equal to 1/4.
x + 2/x becomes 8 + 1/4 which becomes 32/4 + 1/4 which is equal to 33/4.


both solutions are good.
the number can be 1/4 or 8.