Question

设全集U={x|x小于等于5,且x属于N+},集合A={x^2-5x+q=0},B={x^2+px+12=0}.且AUB

Answer 1

全集U={x|x小于等于5,且x属于N+}={1,2,3,4,5}

集合A={x^2-5x+q=0}={x1,x2},则有

x1+x2=5,x1x2=q

集合B={x^2+px+12=0}={x3,x4}

x3+x4=-p,x3x4=12

∵AUB=｛1,4,3｝

∴A∩B=｛4｝,A=｛1,4｝,B=｛4,3｝

∴p=-(3+4)=-7,q=1*4=4