1.设全集U=R.M={m|方程mx^2-x-1=0有实数根}N={n|方程x^2-x+n=0有实数根},求(CuM)∩N2.f(x)=-x^2+2ax与g(x)=a/x在[1,2]上都为减函数,则a范围是?

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1.设全集U=R.M={m|方程mx^2-x-1=0有实数根}N={n|方程x^2-x+n=0有实数根},求(CuM)∩N2.f(x)=-x^2+2ax与g(x)=a/x在[1,2]上都为减函数,则a范围是?

1.设全集U=R.M={m|方程mx^2-x-1=0有实数根}N={n|方程x^2-x+n=0有实数根},求(CuM)∩N2.f(x)=-x^2+2ax与g(x)=a/x在[1,2]上都为减函数,则a范围是?
1.设全集U=R.
M={m|方程mx^2-x-1=0有实数根}
N={n|方程x^2-x+n=0有实数根},求(CuM)∩N
2.f(x)=-x^2+2ax与g(x)=a/x在[1,2]上都为减函数,则a范围是?

1.设全集U=R.M={m|方程mx^2-x-1=0有实数根}N={n|方程x^2-x+n=0有实数根},求(CuM)∩N2.f(x)=-x^2+2ax与g(x)=a/x在[1,2]上都为减函数,则a范围是?
M=[-0.25,+无穷)——CuM=(-无穷,-0.25)
N=(-无穷,0.25)
(CuM)∩N=(-无穷,-0.25)
要使f(x)为减函数,先将f(x)求导,令f′(x)=-2x+2a≤0恒成立.因为x∈[1,2],所以a≤1.
要使g(x)为减函数,则a≥0
所以a∈[0,1]

1对于集合M,当m=0时,x=-1,即0∈M;
当m≠0时,△=1+4m≥0,即m≥- ,且m≠0
∴m≥- ,∴CUM={m|m<- }
而对于集合N,△=1-4n≥0,即n≤ ,∴N={n|n≤ }
∴(CUM)∩N={x|x<- }.