已知X1,X2是方程2x的平方+3x-4=0的两个实数根x1的平方+x2的平方

X1,X2是方程2x的平方+3x-4=0的两个实数根
x1+x2=-3/2
x1x2=-2
x1^2+2x1x2+x^2=9/4
x1^2-2x1x2+x^2=9/4-4x1x2
(x1-x2)^2=41/4
x1-x2=√41/2或x1-x2=-√41/2
（1）当x1-x2=√41/2
x1=(√41/2-3/2)/2=(√41-3)/4
x2=-3/2-(√41-3)/4=-(√41+3)/4
x1^2+x2=((√41-3)/4)^2-(√41+3)/4=(41-2√41+3)/16-(√41+3)/4
=(22-√41)/8-(√41+3)/4=(16-3√41)/8=2-3√41/8
（2）当x1-x2=-√41/2
x1=(-√41/2-3/2)/2=(-√41-3)/4
x2=-3/2-(-√41-3)/4=(√41-3)/4
x1^2+x2=((-√41-3)/4)^2+(√41-3)/4=(41+2√41+3)/16+(√41-3)/4
=(22+√41)/8+(√41-3)/4=(16+3√41)/8=2+3√41/8