Question 143775

Let x=the number
Then 1/x= the reciprocal of the number

x+1/x=13/6  multiply each term by 6x

6x^2+6=13x  subtract 13x from each side

6x^2-13x+6=0------------------quadratic in standard form.  Solve using the quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (13 +- sqrt( 13^2-4*6*6 ))/(2*6) }}} 
{{{x = (13 +- sqrt( 169-144))/(12) }}} 
{{{x = (13 +- sqrt(25))/(12) }}} 
{{{x = (13 +-5)/(12) }}}
{{{x = (13-5)/(12)=8/12=2/3 }}} and
{{{x = (13 +5)/(12)=18/12 =3/2}}} 
This tells us that the number can either be 2/3 or 3/2

CK

2/3+3/2=13/6
4/6+9/6=13/6
13/6=13/6

Hope this helps----ptaylor