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CuA,CuB然后解出A和B.解得:A={-1/3,5},B={=1/3,-3}.
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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CuA,CuB然后解出A和B.解得:A={-1/3,5},B={=1/3,-3}.](/uploads/image/z/2539466-26-6.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%82CuA%2CCuB%E7%84%B6%E5%90%8E%E8%A7%A3%E5%87%BAA%E5%92%8CB.%E8%A7%A3%E5%BE%97%EF%BC%9AA%3D%7B-1%2F3%2C5%7D%2CB%3D%7B%3D1%2F3%2C-3%7D.)
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CuA,CuB然后解出A和B.解得:A={-1/3,5},B={=1/3,-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CuA,CuB
然后解出A和B.
解得:A={-1/3,5},B={=1/3,-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CuA,CuB然后解出A和B.解得:A={-1/3,5},B={=1/3,-3}.
3x^2+px-5=0
1/3-p/3-5=0
p=-14 A={x|3x^2+px-5=0}={-1/3,5} CuA={-3}
3x^2+10x+q=0
1/3-10/3+q=0
q=3 B={x|3x^2+10x+q=0}={-1/3,-3) CuB={5}
因为A∩B={-1/3},所以,-1/3即是A的元素又是B中的元素,把-1/3带进去可求出p和q的值。
因为过程简单,所以不写了,直接写结果。p=-14.q=3.然后解出A和B。
解得: A={-1/3,5},B={=1/3,-3}。
所以CuA ={-3},CuB={5}
-1/3是公共跟
A
x1=-1/3
x1x2=-5/3
x2=5
A={5,-1/3}
B
x1=-1/3
x1+x2=-10/3
x2=-3
B={-3,-1/3}
所以
CuA={-3}
CuB ={5}
A∩B={-1/3},说明x=-1/3是A、B两个集合中方程的根
∴3×(1/9)+p×(-1/3)-5=0,3×(1/9)+10×(-1/3)+q=0
解得,p=-14 , q=3
∴A={x|3x^2+px-5=0}={x|3x^2-14x-5=0}={-1/3,5}
B={x|3x^2+10x+q=0}={x|3x^2+10x+3=0}={-1/3,-3)
∴CuA={-3},CuB={5}