Question 389490
If the number is {{{n}}}, then the
reciprocal is {{{1/n}}}
given:
{{{n + 1/n = 25/12}}}
Multiply both sides by {{{n}}}
{{{n^2 + 1 = (25/12)*n}}}
{{{12n^2 + 12 = 25n}}}
{{{12n^2 - 25n + 12 = 0}}}
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 12}}}
{{{b = -25}}}
{{{c = 12}}}
{{{n = (-(-25) +- sqrt( (-25)^2-4*12*12 ))/(2*12) }}}
{{{n = ( 25 +- sqrt( 625 - 576 ))/24 }}}
{{{n = ( 25 +- sqrt( 49 ))/24 }}}
{{{n = (25 + 7)/24
{{{n = 32/24}}}
{{{n = 4/3}}}
and
{{{n = (25 - 7)/24}}}
{{{n = 18/24}}}
{{{n = 3/4}}}
The answer is either 3/4 or 4/3. That is because one is the reciprocal
of the other
check answer:
{{{n^2 + 1 = (25/12)*n}}}
{{{(4/3)^2 + 1 = (25/12)*(4/3)}}}
{{{16/9 + 9/9 = 25/9}}}
{{{25/9 = 25/9}}}
OK