Question 479892
No one seems to want this problem and I am not too happy with this effort but here it is:
:
Let x = the rational number
Let y = "some positive integer"
:
The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110.
x + {{{1/x}}} = y + {{{69/110}}}
Only y = 4, seems to work out for me here
x + {{{1/x}}} = 4 + {{{69/110}}}
x + {{{1/x}}} = {{{440/110}}} + {{{69/110}}}
x + {{{1/x}}} = {{{509/110}}}
Find x
x + {{{1/x}}} -{{{509/110}}} = 0
Multiply by 110x
110x^2 - 509x + 110 = 0
Using the quadratic formula: a=110, b=-509, c=110
One solution that works x = 4.4 which is {{{44/10}}} so we have:
{{{44/10}}} + {{{10/44}}} = 4 + {{{69/110}}}
Checking it
{{{968/220}}} + {{{50/220) = {{{880/220}}} + {{{138/220}}}
{{{1018/220}}} = {{{1018/220}}}