求两道集合题集合A={y|y²-(a²+a+1)y+a(a²+1)>0} B={y|y²- 6y +8≤0} 若A∩B≠∅ 求a取值A={x|(x+1)/(x+3)<0} B={x|ax²-x+b≤0} 且A∩B=∅ A∪B=R 求a,b的值
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![求两道集合题集合A={y|y²-(a²+a+1)y+a(a²+1)>0} B={y|y²- 6y +8≤0} 若A∩B≠∅ 求a取值A={x|(x+1)/(x+3)<0} B={x|ax²-x+b≤0} 且A∩B=∅ A∪B=R 求a,b的值](/uploads/image/z/10728720-0-0.jpg?t=%E6%B1%82%E4%B8%A4%E9%81%93%E9%9B%86%E5%90%88%E9%A2%98%E9%9B%86%E5%90%88A%3D%7By%7Cy%26%23178%3B-%28a%26%23178%3B%2Ba%2B1%29y%2Ba%28a%26%23178%3B%2B1%29%3E0%7D+B%3D%7By%7Cy%26%23178%3B-+6y+%2B8%E2%89%A40%7D+%E8%8B%A5A%E2%88%A9B%E2%89%A0%26%238709%3B+%E6%B1%82a%E5%8F%96%E5%80%BCA%3D%7Bx%7C%28x%2B1%29%2F%28x%2B3%29%EF%BC%9C0%7D+B%3D%7Bx%7Cax%26%23178%3B-x%2Bb%E2%89%A40%7D+%E4%B8%94A%E2%88%A9B%3D%26%238709%3B+A%E2%88%AAB%3DR+%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC)
求两道集合题集合A={y|y²-(a²+a+1)y+a(a²+1)>0} B={y|y²- 6y +8≤0} 若A∩B≠∅ 求a取值A={x|(x+1)/(x+3)<0} B={x|ax²-x+b≤0} 且A∩B=∅ A∪B=R 求a,b的值
求两道集合题
集合A={y|y²-(a²+a+1)y+a(a²+1)>0} B={y|y²- 6y +8≤0} 若A∩B≠∅ 求a取值
A={x|(x+1)/(x+3)<0} B={x|ax²-x+b≤0} 且A∩B=∅ A∪B=R 求a,b的值
求两道集合题集合A={y|y²-(a²+a+1)y+a(a²+1)>0} B={y|y²- 6y +8≤0} 若A∩B≠∅ 求a取值A={x|(x+1)/(x+3)<0} B={x|ax²-x+b≤0} 且A∩B=∅ A∪B=R 求a,b的值
解,y²- 6y +8≤0,可知2≤y≤4所以B=[2,4]
将y²-(a²+a+1)y+a(a²+1)>0因式分解得:
(y-a)[y-(a^2+1)]>0,由于a^2+1>a(可以通过a^2+1-a凑成平方式得出)
所以y>a^2+1或ya^2+1或y