Răspuns:
a)x^2-5x+4<=0
a=1
b=-5
c=4
Delta=25-16
Delta=9
x
[tex]x =( 5 + \sqrt{9 }) \div 2 = 8 \div 2 = 4 \\ [/tex]
b)(x-3)(2x-1)>=0
[tex]( \times - 3) \geqslant 0 \\ x = 3[/tex]
[tex]2x - 1 \geqslant 0 \\ 2x \geqslant 1 \\ x \geqslant 1 \div 2[/tex]
c)x^2-5/x+4>=0
[tex]x { }^{2} - 5 \geqslant 0 \\ x {?}^{2} \geqslant 5[/tex]
[tex]x \geqslant \sqrt{5} [/tex]
[tex]x + 4 \geqslant 0 \\ x \geqslant - 4[/tex]
d)(1/x+1/x-3)<2
[tex] \frac{2}{x(x - 3)} < 2[/tex]
[tex] \frac{2}{x {?}^{2} - 3x } \geqslant 2[/tex]
2<2x^2+6x
2x^2+6x-2<0
a=2
b=6
c=-2
Delta:36-(-16)=36+16=52
[tex]x = - 6 + \sqrt{52 } \div 4[/tex]
e) (x-2)^2*3(x^2-1)=(x^2-4x+4)(3x^2-3)>=6
x^2-4x+4>=6
x^2-4x-2>=0
a=1
b=-4
c=-2
Delta: 16-(-8)=24
[tex]x = (4+ \sqrt{24} ) \div 2 = 4 + 4 \sqrt{3} \div 2[/tex]
f) 2x-7/5<=x+1/4
8x-28-5x-5/20<=0
3x-32<=0
3x<=32
x<=32/2
g)x-3/7<x+1/2x
(2x(x-3)-2x(x+1))/2x<=0
(2x^2-6x-2x^2+2x)/2x<=0
-4x/2x<=0
2x<=0
x<=0
h)1/8+x/3-2x+1/5<4/x
5/45+15/45-18x+9/45-180/x/45=(20-18x+9-180/x)/45=(29-18x-180/x)/45=
(29-(18x^2-180)/x)/45=(29x-18x^2-180/x)/45
=(29x-18x^2-180)/45x<0
-18x^2-180-29x<0
a=-18
b=-180
c=-29
Delta=30.312
[tex]x = - 180 + \sqrt{30312} \div 36[/tex]
