Question 1112826
{{{ x + 1/x = 10/3 }}}
Multiply both sides by {{{ 3x }}}
{{{ 3x^2 + 3 = 10x }}}
{{{ 3x^2 - 10x + 3 = 0 }}}
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Use the quadratic formula
{{{ x = ( -b +-sqrt( b^2 - 4*a*c ))/ (2a) }}}
{{{ 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 }}}
and
{{{ x = ( 10 - 8 )/6 }}}
{{{ x = 1/3 }}}
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The answers are 3, and 1/3