let $F(a,b,c,d,e,f) = abcdef$ and our constraint is $a^2+b^2+c^2+d^2+e^2+f^2=6$ ,$a+b+c+d+e+f=0$ then lagrange
we get
$abcdef = 2a^2k +ma=2b^2.k+m.b =.....=2f^2.k+mf$ but this is quite complicated to do is there any elegant way like trig sub or something
for $a,b,c,d,e,f$ real numbers