m、n为何值时方程x²+2(m+1)x+3m²+4mn+4n²+2=0有两个相等的实数根

2024-12-31 22:41:52
推荐回答(2个)
回答1:

计算Δ=0
4(m+1)²-4(3m²+4mn+4n²+2)=0
2m²+4mn+4n²-2m+1=0
(m-1)²+(m+2n)²=0
m=1且m=-2n
所以m=1,n=-1/2

回答2:

△=0
4(m+1)^2-4(3m^2+4mn+4n^2+2)=0
-8m^2+8m-16mn-16n^2-4=0
-4m^2-16mn-16n^2-4m^2+8m-4=0
4(m+2n)^2+4(m-1)^2=0
m=1,n=-1/2