(X-3)(X+3)<1 救解的过程 (2X-1)(X-3)>-2 3-2x⼀2-3X〈等于1 根号8-X -根号2X-3>0 求解的过程

2024-12-19 02:11:21
推荐回答(2个)
回答1:

(x-3)(x+3)<1
x^2-9<1
x^2<10
-√10
(2x-1)(x-3)>-2
2x^2-7x+3>-2
2x^2-7x+5>0
(2x-5)(x-1)>0
x<1,或 x>5/2 (大于取两边)

(3-2x)/(2-3x)<=1
(3-2x)/(2-3x)-1<=0
[(3-2x)-(2-3x)]/(2-3x)<=0
(x+1)/(2-3x)<=0
-1<=x<2/3 (小于取中间,分母不为0)

√(8-x)-√(2x-3)>0
√(8-x)>√(2x-3) (两边平方,得:)
8-x>2x-3 且 8-x>=0且 2x-3>=0 (根式有意义)
-3x>-11 且 x<=8 且 x>=3/2
x<11/3 且 x<=8 且 x>=3/2
所以 3/2<=x<11/3 (利用数轴取交集)

回答2:

1)X^2-9<1 x^2<10 所以X属于(-根号10,根号10)
2)2x^2-6x-x+3>-2 2x^2-7x+5>0 (2x-5)(x-1)>0 所以x属于(-无穷,1)U(5/2,正无穷)
3)(3-2x-2+3x)/(2-3x)<=0 (x+1)/(3x-2)>=0 (x+1)(3x-2)>=0 所以x属于(-无穷,-1]U(2/3,正无穷)
4)8-x>2x-3 3x<11 x<11/3 8-x>0 x<8 2x-3>0 x>3/2 所以x属于(3/2,11/3)