Question

设全集U={-1/3,5,-3}，集合A={x|3x^2+px-5=0}与集合B={x|3x^2+10x+q=0}，且A∩B={-1/3}，

设全集U={-1/3,5,-3}，集合A={x|3x^2+px-5=0}与集合B={x|3x^2+10x+q=0}，且A∩B={-1/3},求P,Q的值 ，求CuA,CuB

Answer 1

A={x|3x^2+px-5=0}
B={x|3x^2+10x+q=0}

A∩B={-1/3}
=> -1/3 ∈A and -1/3 ∈B

-1/3 ∈A =>
3x^2+px-5=0
1/3-p/3 -5 =0
p= -14

-1/3 ∈B =>
1/3-10/3+q=0
q=3

p=-14
A = {x|3x^2-14x-5=0}
= {-1/3, 5}
CuA ={-3}

q=3
B={x|3x^2+10x+3=0}
={-1/3, -3}
CuB={5}

Answer 2

∵A∩B={-1/3} ∴将-1/3分别代入A B的方程，得出p=-14,q=3
用韦达定理算出A={5，-1/3} B={-3，-1/3}
∴CuA={-3},CuB={5}