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
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![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](/uploads/image/z/3942966-30-6.jpg?t=%E8%AE%BE%E5%85%A8%E9%9B%86U%3D%7B-1%2F3%2C5%2C-3%7D%2C%E9%9B%86%E5%90%88A%3D%7Bx%7C3x%5E2%2Bpx-5%3D0%7D%E4%B8%8E%E9%9B%86%E5%90%88B%3D%7Bx%7C3x%5E2%2B10x%2Bq%3D0%7D%2C%E4%B8%94A%E2%88%A9B%3D%7B-1%2F3%7D%2C%E6%B1%82P%2CQ%E7%9A%84%E5%80%BC+%2C%E6%B1%82CuA%2CCuB)
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
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
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
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}
∵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}
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