已知关于x的一元二次方程x²+2（m+1)x+(3m²+4mn+4n²+2)=0有实根,求3m²+2n³的值

有实根,则△≥0
4(m+1)²-4(3m²+4mn+4n²+2)≥0
m²+2m+1-3m²-4mn-4n²-2≥0
2m²+4mn+4n²-2m+1≤0
(m²+4mn+4n²)+(m²-2m+1)≤0
(m+2n)²+(m-1)²≤0
平方数都是非负数,两个非负数的和小于等于0,只能都是0
m+2n=0
m-1=0
解得:m=1,n=-0.5
3m²+2n³
=3×1+2×(-0.5)³
=3-0.25
=2.75