已知x的一元二次方程x²+2(m+1)+3m²+4mn+4n²+2=0有实数根,则3m²+2n²的值为多少
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![已知x的一元二次方程x²+2(m+1)+3m²+4mn+4n²+2=0有实数根,则3m²+2n²的值为多少](/uploads/image/z/1240757-53-7.jpg?t=%E5%B7%B2%E7%9F%A5x%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%28m%2B1%29%2B3m%26%23178%3B%2B4mn%2B4n%26%23178%3B%2B2%3D0%E6%9C%89%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E5%88%993m%26%23178%3B%2B2n%26%23178%3B%E7%9A%84%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91)
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已知x的一元二次方程x²+2(m+1)+3m²+4mn+4n²+2=0有实数根,则3m²+2n²的值为多少
已知x的一元二次方程x²+2(m+1)+3m²+4mn+4n²+2=0有实数根,则3m²+2n²的值为多少
已知x的一元二次方程x²+2(m+1)+3m²+4mn+4n²+2=0有实数根,则3m²+2n²的值为多少
4(m+1)^2-4(3m^2+4mn+4n^2+2)≥0
m^2+2m+1-3m^2-4mn-4n^2-2)≥0
-2m^2-4mn-4n^2+2m-1≥0
2m^2+4mn+4n^2-2m+1≤0
m^2+4mn+4n^2+m^-2m+1≤0
(m+2n)^2+(m-1)^2≤0
平方和非负,所以
(m+2n)^2=0,(m-1)^2=0
m=-2n,m=1
m=1,n=11/2
3m²+2n²=3*1^2+2*(-1/2)^2=7/2
3m²+2n²的值为 7/2