Question 187058
{{{x + 1/x = 10/3}}}
Multiply both sides by {{{3x}}}
{{{3x^2 + 3 = 10x}}}
{{{3x^2 - 10x + 3 = 0}}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 3}}}
{{{b = -10}}}
{{{c = 3}}}
{{{x = (-(-10) +- sqrt( (-10)^2-4*3*3 ))/(2*3) }}}
{{{x = (10 +- sqrt( 100 - 36 ))/6 }}}
{{{x = (10 +- sqrt( 64 ))/6 }}}
{{{x = (10 +- 8)/6 }}}
{{{x = 3}}}
{{{x = 1/3}}}
The sum of 3 and it's reciprocal is 10/3
also, the sum of 1/3 and it's reciprocal is 10/3