解不等式:(1)x^2-x+3>0 (2)x^2-7x+3<=0

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解不等式:(1)x^2-x+3>0 (2)x^2-7x+3<=0

(1)判别式<0 所以x^2-x+3永远在x轴上方,即对一切x都成立
(2)用求根公式
(7-√37)/2<=x<=(7+√37)/2

(1)x^2-x+3=(x-1/2)^2+11/4>0恒成立,所以解为一切实数;
(2)x^2-7x+3=(x-7/2)^2-37/4<=0
7/2-(37/4)^0.5<=x<=7/2+(37/4)^0.5

答案(1)因为deter小于0,解集为全体实数

(1)x^2-x+3>0
x^2-x+1/4+11/4>0
(x-1/2)^2+11/4>0
故x为全体实数
x^2-7x+3<=0
(7-√37)/2≤X≥(7+√37)/2