Mate

Ejercicio 3
x x-1≥2x-1≥0
xx-1- 2x-1≥0
xx-1-2(x-1)(x-1)≥0
x-1(x-2)(x-1)2≥0
(x-2)(x-1)≥0
x-2(x-1)≥0
r1= +2; r2=+1
+ - + -∞ +2 +1 +∞
c.s.(<-∞;+2>U<+1;+∞>)

Ejercicio 4
x4-25x2-144<0
-x216-x29-16x2-9x2-25x2
16-x29-x2<0
x+44-xx+33-x<0
r1=+4; r2=-4; r3=+3; r4=-3
+ - +- + -∞ -4 -3 +3 +4 +∞
c.s.(<-4;-3>U<+3;+4>)

Ejercicio 5
x4-16x2-225≥0
x2-25x29-25x2+9x2-16x2
x2-25(x2+9)≥0
x-5x+5(x2+9)≥0
r1=+5; r2=-5; r3=-3i; r4=+3i

+ - + -∞ -5 +5 +∞
c.s(<-∞;-5>U<+5;+∞>)

Ejercicio 6
x2-1x2-4≤0
x+1(x-1)x+2(x-2)≤0x+1x-1x+2(x-2)≤0

r1=-1; r2=+1; r3=+2; r4=-2

+ - + - + -∞ -2 -1 +1 +2 +∞
c.s.(<-2;-1>U<+1;+2>)

Ejercicio 7
x3-5x2+ 6x≤0
x(x2-5x+6)≤0
x-3x-2-3x-2x-5x
xx-3(x-2)≤0
r1=0; r2=+3; r3=+2
- + - +-∞ 0+2 +3 +∞
c.s.(<-∞;0>U<+2;+3>)

Ejercicio 8
x3-5x2+ 6x>0
x(x2-5x+6)>0
x-3x-2-3x-2x-5x
xx-3(x-2)>0
r1=0; r2=+3; r3=+2
- + - +-∞ 0 +2 +3 +∞
c.s.(<0;+2>U<+3;+∞>)

Ejercicio 9
x2+3x-10x2+x-2<0
x+5(x-2)x-1(x+2)<0x+5x-2x-1(x+2)<0
r1=-5; r2=+2; r3=+1; r4=-2
+ - + - + -∞ -5 -2 +1 +2 +∞
c.s.(<-5;-2>U<+1;+2>)

Ejercicio 10
(x-1)3+2x<2
(x-1)3+ 2x-2<0
(x-1)3+2(x-1)<0
x-1(x-12+2)<0
x-1(x2+2x-1+2)<0
x-1(x+1)2<0r1=+1; r2=-1 multiplicidad de 2
- + -∞ -1 +1 +∞
c.s.( <-∞;+1>--1 )


Ejercicio 11
(x-1)3+2x>2
(x-1)3+ 2x-2>0
(x-1)3+2(x-1)>0
x-1(x-12+2)>0
x-1(x2+2x-1+2)>0
x-1(x+1)2>0
r1=+1; r2=-1 multiplicidad de 2
-+ -∞ -1 +1 +∞

c.s.(<+1;+∞>--1 )

Ejercicio 12
-2x3-4x2-2x≥0
-2 -4 -2-1 ↓ 2 2 -2 -2 0
r1=-1±3i2 ; r2=-1; r3=0
+ - + -∞ -10 +∞
c.s.(<-∞;-1>U<0;+∞>)

Ejercicio 13
x2-1-x2+2x-1≤0
x-1(x+1)x-1(1-x)≤0
(x+1)(1-x)≤0
x+1(1-X)≤0
r1=-1; r2=+1
+ - + -∞ -1 +1 +∞
c.s.(<-1;+1>)

Ejercicio 14

3x2+4<x4+3x3+3x
-x4-3x3+3x2-3x+4<0
r1=-1; r2=+1+ - + -∞ -1 +1 +∞

c.s.(<-1;+1>

Ejercicio 15
x2+4x2-4≥0
(x2+4)x+2(x-2)≥0
x2+4x+2(x-2)≥0
r1=-2; r2=+2; r3=+2i; r4=-2i
+ - + -∞ -2 +2 +∞c.s.(<-∞:-2>U<+2;+∞>

Ejercicio 16
x4-3x3-13x2+9x+30>0
1 -3 -13 9 30 -2 ↓ -2 +10 6 -30 1 -5 -3 15 0+5 ↓ 5 0 15 1 0 3 0
x2+0x-3=0
x2-3=0 ; x=±3
r1=-2; r2=+5; r3=-3; r4=+3
+ -...