Ecuaciones

1.- x/3+2x/4-x/5+3x/2=1

(20x+30x-12x+90x)/60=1
20x+30x-12x+90x=60
128x=60
x=60/128

2.- (w+9)/(w-2)=(w-3)/(w+4)
(w+9)(w+4)=(w-3)(w-2)
w^2+4w+9w+36=w^2-2w-3w+6
13w+5w=-36+6
18w=-30
w=(-30)/18

3.- 1/((x+2)+2/((x-3) )=6
((x-3)+2(x+2))/((x+2) (x-3) )=6
x-3+2x+2=6(x+2)(x+3)
2x^2-1=6(x^2-3x+2-6
2x^2-6x^2+18x-12x-1+36=0
-4x^2+6x+35=0
x=(-b±√(b^2-4ac))/2a
x=(4±√(〖36〗^2-4(-4)(35)))/(-8)=
x=(4±√(36+560))/(-8)
x=(4±√596)/(-8)
x=(4±24.41)/(-8)
x_(1=-3.55)
x_(2=2.55)

4.- (z^3-43)/(z-7)=80
z^3-343÷z-7=z^2+7z+49
z^2+7z+49=80
z^2+7z+49-80=0
z^2+7z-31=0
z=(-b±√(b^2-4ac))/2a
z=(-7±√(49-4(1)(-31)))/2
z=(-7±√(4+124))/2
z=(-7±√173)/2
z_1=3.075
z_(2=)-10.075

5.- √x+36=(x+4)
(√x+36)^2=(x+4)^2
x+36=x^2+8x+16
-x^2-7x+20=0
x=(-b±√(b^2-4ac))/2ax=(-7±√(49-4(-1)(20) ))/(-2)
x=(-7±√(49+80))/(-2)
x=(-7±√129)/(-2)
x_1=-9.175
x_2=2.175

6.- 5+√x+18=x+7
(5+√x+18)^2=(x+7)^2
25+x+18=x^2+14x+49
25+x+18-x^2-14x-49=0
-x^2-13x-6=0
x=(-b±√(b^2-4ac))/2a
x=(13±√(169-24))/(-2)
x=(13±√145)/(-2)
x_1=-12.52
x_2=-.48

7.- 2x^2-3x/4-1/8=0
x=(-b±√(b^2-4ac))/2a
x=(3⁄4±√(9⁄16-4(2)(-1⁄8) ))/4
x=(3⁄4±√(25⁄16))/4
x=(0.75±1.25)/4
x_1=0.5
x_2=-0.125

8.-(x+1/6) (x-1/7)=4
(x+1⁄6)=4 (x-1⁄7)=4
x+1⁄6-4=0 x-1⁄7-4=0
x-23/6=0 x-29/7=0

9.- x^(2+2/3 x+1/9)/(x+1/3)=2
x^2+2/3 x+1/9=2(x+1/3)
x^2+2/3 x+1/9=2x+2/3
x^2+2/3 x+1/9-2x-2/3=0
x^2-4/3-5/9=0
x=(-b±√(b^2-4ac))/2a
x=(4⁄3±√(16⁄9-20⁄9))/2
x=(4⁄3±√4)/2
x=(4⁄3±2)/2
x_1=1.665
x_2=-0.335

10.- x^3-20x+1=97
x^3-20x+1-97=0
x^3-20x-96=0
Por tanteo x=6x^3-20x-96÷x-6=x^2+6x+16
x^3-20x-96=(x-6)(x^2+6x+16)=0
(x-6)(x^2+6x+16)=0
x-6=0
x_1=6
x^2+6x+16=0
x=(-b±√(b^2-4ac))/2a
x=(-6±√(36-4(1)(16) ))/2
x=(-6±√(-28))/2
x=(6±√(28 √(-1)) )/2
x=(-6±5.29 ¡)/2
x_2=-3+2.645¡
x_3=-3-2.645¡

11.- x^3-512=0
x^3=512
∛(x^3 )=∛512
x=8
x^3-512÷x-8=x^2 8x+64
(x-8)(x^2+8x+64)=x^3-512
(x-8)(x^2+8x+64)=x^3-512
x-8=0
x_1=8
x^2+8x+64=0
x=(-b±√(b^2-4ac))/2ax=(-8±√(64-4(1)(64) ))/2
x=(-8±√(64-256))/2
x=(-8±√(-192))/2
x=(-8±√192 √(-1 ))/2
x=(-8±13.85¡)/2
x_2=-4+6.925¡
x_3=-4-6.925¡

12.- x^3-14x^2-14x+196=0
x^2 (x-14)-14(x-14)=0
(x-14)(x^2-14)=0
x-14=0
x_1=14
x^2-14=0
x^2=14
√(x^2 )=√(14 )
x=±3.74
x_2= +3.74
x_3=-3.74

13.- x^3-15x=0
(x)(x^2-15)=0
x_1=0
x^2-15=0
x^2=15
√(x^2 )=√(15 )
x=±3.87
x_2= +3.87
x_3=-3.87

14.- x^4-6561=0x^4=6561
4√(x^4 )= 4√6561
x=9
x^4-6561 ÷ x-9=x^3+9x^2+81x+729
(x-9) (x^4-6561=x^3+9x^2+81x+729)=0
x_1=9
x^3+9x^2+81x+729=0
x^2 (x+9)+81(x+9)=0
(x+9)(x^2+81)=0
x+9=0
x_1=-9
x^2+81=0
x^2=-81
√(x^2 )=√(81 ) √(-1 )
x=±9i
x_2= +9i
x_3=-9i
15.- x^4-2x^2-8=0
x=2
(2)^4-2(〖2)〗^2-8=0
16-8-8=0
0=0
x^4-2x^2-8 ÷ x-2= x^3+2x^2+2x-4
x^4-2x^2-8=( x-2)(x^3+2x^2+2x-4)
(x-2)(x^3+2x^2+2x-4)=0
x-2=0
x_1=2
x^3+2x^2+2x-4=0
x^2 (x+2)2(x+2)
(x+2)2(x+2)=0
x_2=-2
x^2 +2=0
x^2=- 2
√(x^2 )=±√(-2 )
x=±√(-2 )
x=±√(2 ) √(-1 )
x_3=+1.4i
x_4=-1.4i
16.- 〖4x〗^4-x^3=0
〖(x〗^3)( 4x-1)=0
x_3=0
x.x.x=0
x_1=0
x_2=0
x_3=0
4x-1=0
4x=1
x_4=1/4
17.- (x+1)^4=x^4+4x^3
x^4+4x^3 (1)+〖6x〗^2 (1) 〖^2〗+4x+1=x^4+4x^3
〖6x〗^2+4x+1=0
x=(-b±√(b^2-4ac))/2a
x=(-4±√(16-4(6)(1)))/12x=(-4±√(16-24))/12
x=(-4±√(8 -1))/12
x_1=-0.33+0.235i
x_2=-0.33-0.235i

18.- x^(3/2)-5=0
x^□(3/2)=5
〖(x〗^□(3/2) )^□(2/3)=5^□(2/3)
x^□(6/6)=∛(5^2 )
x=2.92
19.- x^5-〖2x〗^3=0
(x^3 )(x^2-2)=0
x^3=0
x*x*x=0
x_1=0
x_2=0
x_3=0
x^2-2=0
x^2=2
√(x^2 )=±√2
x=±1.41
x_4= +1.41
x_5=-1.41
20.-∛(x^(3 ) )+8=(x+2)
(∛(x^(3 ) )+8)〖^3〗=(x+2) 〖^3〗
x^3+8=x^3+〖6x〗^2+12x+8
0=〖6x〗^2+12x(〖6x〗^2+12x)/6=0
x^2+2x=0
(x) (x+2)=0
x_1=0
x+2=0
x_2=-2

21.-RESOLVER POR ELIMINACIÒN DE GAUSS
2x+y-3z=5
3x-2y+2z=5
5x-3y-z=16

-3(2x+y-3z=5)
2 (3x-2y+2z=5)

-6x-3y+9z=-15
6x-4y+4z= 10
-7y+13z=-5

-5(2x+y-3z=5)
2(5x-3y-z=16)

-10x-5y+15z=-25
10x-6y+2z= 32
-11y+13z= 7

-11(-7y+13z=-5)
7(-11y+13z= 7)

77y-143z=55
-77y+91z=49
-52z =104...