百度知道求一道数学题解答

1.当a=0时,f(x)=|2x+1|+|2x+3|>=6
(a)当x属于(-无穷,-3/2]时,f(x)=-2x-1+(-2x-3)=-4x-4>=6,得x属于(-无穷,-5/2]
(b)当x属于(-3/2,-1/2]时,f(x)=-2x-1+2x+3=2,无解
(c)当x属于(-1/2,+无穷)时,f(x)=4x+4>=6,x属于[1/2,+无穷)
综上:x属于(-无穷,-5/2]U[1/2,+无穷)
2.原式化为:|2x+1|+|2x+3|>=a^2-a
设左边的新函数为g(x)=|2x+1|+|2x+3|,右边为h(a)=a^2-a
(a)当x属于(-无穷,-3/2]时,g(x)=-2x-1+(-2x-3)=-4x-4,g(x)的范围为[2,+无穷)
(b)当x属于(-3/2,-1/2]时,g(x)=-2x-1+2x+3=2
(c)当x属于(-1/2,+无穷)时,g(x)=4x+4,范围为[2,+无穷)
所以g(x)min=2
因此,a^2-a