已知一元二次方程X^2-4X+2=0的两个根分别为X1 X2 求代数式X2/X1+X1/X2的值

∵X1、 X2 是方程X²-4X+2=0的两个根
∴X1+X2=4,X1·X2=2
X2/X1+X1/X2
=X2²/(X1·X2)+X1²/(X1·X2)
=(X1²+X2²)/(X1·X2)
=[(X1+X2)²-2X1·X2)]/(X1·X2)
=(4²-2×2)/2
=(16-4)/2
=12/2
=6