Question 209223
x = the number
1/x is the reciprocal of the number
-----
x - (1/x) = 9/20
multiply both sides by x to get:
x^2 - 1 = (9/20)*x
subtract (9/20)*x from each side of the equation to get:
x^2 - (9/20)*x - 1 = 0
multiply both sides of the equation by 20 to get:
20x^2 - 9x - 20 = 0
-----
using the quadratic formula of {{{(-b +- sqrt(b^2-4ac))/(2a)}}} gets me:
x = 50/40
or:
x = -32/40
-----
x = -32/40 is rejected because it is not positive and the problem stated that it had to be a positive fraction.
-----
your answer is x = 50/40 which is the same as:
x = 5/4
-----
to confirm this answer is correct, substitute in the original equations.
-----
if we let x = 5/4, then:
x - (1/x) = 9/20 becomes:
{{{(5/4) - (1/(5/4)) = 9/20}}}
this is the same as:
{{{(5/4) - (4/5) = 9/20}}}
this becomes:
{{{(25-16)/20 = 9/20}}}
which becomes:
{{{9/20 = 9/20}}} confirming that x = 5/4 is good.
-----
your question was:
find the sum of the fraction and it's reciprocal.
-----
the answer is:
-----
if x = 5/4, then 1/x = 4/5 and the sum is 5/4 + 4/5 = (25+16)/20 = 41/20
-----