2x²+3x-1=0
donc x1+x2=-3/2 et x1x2=-1/2
donc (x1+x2)²=9/4 et x1²x2²=1/4
donc x1²+x2²+2x1x2=9/4
donc x1²+x2²=13/4
(x1-x2)²=x1²+x2²-2x1x2=13/4+1=17/4
1/x1+1/x2=(x1+x2)/(x1x2)
=(-3/2)/(-1/2)=3
1/(x1-1)+1/(x2-1)
=(x1-1+x2-1)/((x1-1)(x2-1)
=(x1+x2-2)/((x1-1)(x2-1))
=(x1+x2-2)/((x1x2-(x1+x2)+1)
=(-3/2-2)/(-1/2+3/2+1)
=-7/4
