设p:实数x满足x^2-4ax+3a^20,命题q:x满足x^2-x-60(1)若a=1且p交q为真,求实数x的取值范围;(2)若非p是非q的充分不必要条件,求实数a的取值范围
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![设p:实数x满足x^2-4ax+3a^20,命题q:x满足x^2-x-60(1)若a=1且p交q为真,求实数x的取值范围;(2)若非p是非q的充分不必要条件,求实数a的取值范围](/uploads/image/z/12490671-39-1.jpg?t=%E8%AE%BEp%EF%BC%9A%E5%AE%9E%E6%95%B0x%E6%BB%A1%E8%B6%B3x%5E2-4ax%2B3a%5E20%2C%E5%91%BD%E9%A2%98q%EF%BC%9Ax%E6%BB%A1%E8%B6%B3x%5E2-x-60%281%29%E8%8B%A5a%3D1%E4%B8%94p%E4%BA%A4q%E4%B8%BA%E7%9C%9F%2C%E6%B1%82%E5%AE%9E%E6%95%B0x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%3B%282%29%E8%8B%A5%E9%9D%9Ep%E6%98%AF%E9%9D%9Eq%E7%9A%84%E5%85%85%E5%88%86%E4%B8%8D%E5%BF%85%E8%A6%81%E6%9D%A1%E4%BB%B6%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
设p:实数x满足x^2-4ax+3a^20,命题q:x满足x^2-x-60(1)若a=1且p交q为真,求实数x的取值范围;(2)若非p是非q的充分不必要条件,求实数a的取值范围
设p:实数x满足x^2-4ax+3a^20,命题q:x满足x^2-x-60
(1)若a=1且p交q为真,求实数x的取值范围;
(2)若非p是非q的充分不必要条件,求实数a的取值范围
设p:实数x满足x^2-4ax+3a^20,命题q:x满足x^2-x-60(1)若a=1且p交q为真,求实数x的取值范围;(2)若非p是非q的充分不必要条件,求实数a的取值范围
解:因x^2-x-6<=0即(x-3)(x+2)<=0,所以-2<=x<=3;又因x^2+2x-8>0 即(x-2)(x+4)>0,所以x>2或x<-4
故q:x<-4或x>=-2
p:实数x满足x^2-4ax+3a^2<0(a<0)即(x-a)
(x-3a)<0(a<0),故p:3a
即p推出q,但q推不出p
所以-2=<3a<0或a<=-4
所以a的取值范围为[-2/3,0)并(-无穷大,-4]
设命题p:实数x满足x^2-4ax+3a^2
设p:实数x满足x^2-4ax+3a^2
设p:实数x满足x^2-4ax+3a^2
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