Question 1043983
If u and v are the roots of the equation of {{{ax^2+bx+c=0}}}, prove that {{{u^2+v^2 = (b^2-2ac)/a^2}}}.

 Solution

sum root=u+v=b/a
product root=uv=c/a
{{{(u+v)^2=b^2/a^2}}}
{{{u^2+v^2=b^2/a^2-2uv}}}
but uv=c/a
then
{{{u^2+v^2=b^2/a^2-2*c/a}}}
take the l.c.m and get
{{{u^2+v^2 = (b^2-2ac)/a^2}}}