Question

设集合A=｛x/x2-ax+a2-19=0},B{x/x2-5x+6=0}.C={x/x2+2x-8=0},若空集真包含

Answer 1

A=｛x|x2-ax+a2-19=0},

B={x|x2-5x+6=0}

= {x| (x-2)(x-3) =0 }

= {2,3}

C={x|x2+2x-8=0}

={ x| (x+4)(x-2)=0 }

= {-4,2}

if A∩B=ø

=> 2,3 不属于A

for x=2

4-2a+a2-19 ≠ 0

a2-2a-15≠ 0

(a-5)(a+3)≠ 0

a ≠ 5 or a ≠ -3

for x=3

9-3a+a2-19 ≠ 0

a2-3a-10 ≠ 0

(a-5)(a+2)≠ 0

a ≠ 5 and a ≠ -2

and A∩C=ø

=> -4,2 不属于 A

for x=-4

16+4a+a2-19 ≠ 0

a2+4a-3 ≠ 0

a ≠ -2+√7 or and a ≠ -2-√7

for x=2,we have a ≠ 5 or a ≠ -3

we have

(a ≠ 5 or a ≠ -3) and (a ≠ 5 and a ≠ -2) and (a ≠ -2+√7 or and a ≠ -2-√7)

ie a ≠ 5 and a ≠ -3 and a ≠ -2 and a ≠ -2+√7 and a ≠ -2-√7 #