Question 982120


Let &nbsp;<B>x</B>&nbsp; be our rational number. 

Then its reciprocal is &nbsp;{{{1/x}}}, &nbsp;and the equation is 

{{{x}}} + {{{1/x}}} = {{{13/6}}}.


Multiply both sides by &nbsp;{{{6x}}}. &nbsp;You will get a quadratic equation 


{{{6x^2}}} + {{{6}}} = {{{13x}}}, &nbsp;or


{{{6x^2}}} - {{{13x}}} + {{{6}}} = {{{0}}}.


Solve it using the quadratic formula. &nbsp;You will get the roots


{{{x[1]}}} = {{{3/2}}} &nbsp;and&nbsp; {{{x[2]}}} = {{{2/3}}}.


<B>Check</B>: &nbsp;&nbsp;{{{3/2}}} + {{{2/3}}} = {{{(9+4)/6}}} = {{{13/6}}}.


<B>Answer</B>. &nbsp;{{{x[1]}}} = {{{3/2}}} and {{{x[2]}}} = {{{2/3}}}.