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
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![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](/uploads/image/z/1963747-19-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%85%B3%E4%BA%8Ex%E7%9A%84%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bx%26%23178%3B%2B2%EF%BC%88m%2B1%29x%2B%283m%26%23178%3B%2B4mn%2B4n%26%23178%3B%2B2%29%3D0%E6%9C%89%E5%AE%9E%E6%A0%B9%2C%E6%B1%823m%26%23178%3B%2B2n%26%23179%3B%E7%9A%84%E5%80%BC)
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
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
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