已知U=R,集合P={x|x=a²+4a+1,a∈R},Q={y|y=-b²+2b+3,B∈R},求

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已知U=R,集合P={x|x=a²+4a+1,a∈R},Q={y|y=-b²+2b+3,B∈R},求P∩Q和P∪CuQ 各位大虾对小弟说下吧

P={x|x=a²+4a+1,a∈R},
Q={y|y=-b²+2b+3,b∈R}
P∩Q =>
a²+4a+1 = =-a²+2a+3
2a²+2a-2=0
a²+a-1=0
a=(-1+√5)/2 or (-1-√5)/2
P={x|x=a²+4a+1,a∈R},
for a=(-1+√5)/2,
x= (-1+√5)^2/4 + 2(-1+√5) +1
= (3-√5)/2 + 2(-1+√5) +1
= (1 + 3√5)/2
for a=(-1-√5)/2
x=(-1-√5)^2/4 + 2(-1-√5) +1
= (3+√5)/2 + 2(-1-√5) +1
= (1-3√5)/2
P∩Q = {(1-3√5)/2,(1+3√5)/2}
Q ={y|y =-b²+2b+3,b∈R}
y =-b²+2b+3,b∈R
=> y is cts on R
y∈（-∞,∞)
CuQ= ø
P∪CuQ = P
= {x|x=a²+4a+1,a∈R},

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