Question 890739
Sum of reciprocals of roots of 3x^2+7x+k is -7/3.  Find k.


{{{x=(-7+- sqrt(49-4*3*k))/6}}}
{{{x=(-7-sqrt(49-12k))/6}}}  or  {{{x=(-7+sqrt(49-12k))/6}}}


{{{-6/(7+sqrt(49-12k))+6/(-7+sqrt(49-12k))=-7/3}}} according to specification in question.
{{{-6/(sqrt(49-12k)+7)+6/(sqrt(49-12k)-7)=-7/3}}}
Multiply left and right by lowest common denominator...
{{{-6*3(sqrt(49-12k)-7)+6*3(sqrt(49-12k)+7)=-7((49-12k)-49)}}}
{{{-18sqrt(49-12k)+18*7+18sqrt(49-12k)+18*7=7*12k}}}
{{{2*18*7=7*12k}}}
{{{2*18=12k}}}
{{{2*6=4k}}}
{{{highlight(highlight(k=3))}}}