Question 198557
The sum of a number and its reciprocal is 34/15. Find the number.
:
x + {{{1/x}}} = {{{34/15}}}
Multiply equation by 15x, results
15x(x) + 15(1) = 34x
:
Arrange as a quadratic equation
15x^2 - 34x + 15 = 0
Factors to:
(5x - 3)(3x - 5) = 0
Two solutions
5x = 3
x = {{{3/5}}}
and
3x = 5
x = {{{5/3}}}
;
;
Check solution using the 1st solution
{{{3/5}}} + {{{5/3}}} = 
{{{9/15}}} + {{{25/15}}} = {{{34/15}}}