Solucion Taller De Ecuaciones
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SOLUCION TALLER DE ECUACIONES 1. 2(2x+3) = x+1 4x +6= x+1 4x-x=1-6 3x=-5 X=-5 3 2. (x+2)2 =x+3
2+x (X+2) = (x+3) (2+x) (X+2) (2+x) = (x+3) 2x+x2+4+2x = x+3 X2+4x+4=x+3 X2+4x-4-x-3=ϕ X2+3x+1= ϕ x=-b±b2-4ac2a
x=-3±32-4(1)(1)2
x=-3±52
X1= -3+√5 =0.4 2 X2= -3-√5 =2.6 2
3. (y+2) (3+y) = 1+5y
3 3y+y2+6+2y= 1+5y 3 5y+y2+6= 1+5y 3 3(5y+y2+6)= 1+5y 15y+3y2+18=1+5y 15y+3y2+18-1=5y 15y+3y+17y=5y 15y-5y+3y2+17= ϕ x=-b±b2-4ac2a 4. 3x+2 - 5x+4 = 6x-1 + 3x-2
4
8
3
5
8(3x+2) – 4(5x+4) = 2(6x-1) + 5(3x-2) 32
10
24x+16-2ox-16 = 12x-2+15x-10 32
4x = 27x-12 32
10
10 (4x) = 32(27x-12) 40x
864x-384
10
X=-824=-384
X=-384= x= -96 -824
5. [(3x+4)3]
X = -48
-206
- 103
(2-x) =Ø
[27x+36] (2-x) = Ø 54x+72- 27x2-36x= Ø -27x2+18x+72= Ø x=-b±b2-4ac2a x=-18±182-4-27(72)2(-27)
x=-18±8100-54
x=-18±90 -54
x=
6.
72 -54
x= -4 3
1 2x+1
+ 2 + 3 =Ø (3x+5) 1-x
2x+1 1
+ 3x+5 + 1-x = Ø 2 3
(2x+1) + (2-2x+9x+15) = Ø 6 12+6+2-2x+9x+15= Ø
-2x+9x= -15-12-6-2 7x= -35 7 X=-35 7
7. 1
=
1 + 3 2x 2x+1
1
-2 3x+1 3x+2
=
2x + 2x+1 1
3
1
1
1
=
6x+2x+1 3
1
3x+1
- 3x+2
2
1
1
6x+2-3x+2 2
1
=
1
3(6x+2x+1)
1
= 18x+6x+3
1
2 (6x+2-3x+2)
1 12x+4-6x+4
=
1
24x+3
6x+8
1
24x+3
6x+8-24x+3= Ø -18x+11= Ø X= 11 -18
1=Ø 6x+8
2+x (X+2) = (x+3) (2+x) (X+2) (2+x) = (x+3) 2x+x2+4+2x = x+3 X2+4x+4=x+3 X2+4x-4-x-3=ϕ X2+3x+1= ϕ x=-b±b2-4ac2a
x=-3±32-4(1)(1)2
x=-3±52
X1= -3+√5 =0.4 2 X2= -3-√5 =2.6 2
3. (y+2) (3+y) = 1+5y
3 3y+y2+6+2y= 1+5y 3 5y+y2+6= 1+5y 3 3(5y+y2+6)= 1+5y 15y+3y2+18=1+5y 15y+3y2+18-1=5y 15y+3y+17y=5y 15y-5y+3y2+17= ϕ x=-b±b2-4ac2a 4. 3x+2 - 5x+4 = 6x-1 + 3x-2
4
8
3
5
8(3x+2) – 4(5x+4) = 2(6x-1) + 5(3x-2) 32
10
24x+16-2ox-16 = 12x-2+15x-10 32
4x = 27x-12 32
10
10 (4x) = 32(27x-12) 40x
864x-384
10
X=-824=-384
X=-384= x= -96 -824
5. [(3x+4)3]
X = -48
-206
- 103
(2-x) =Ø
[27x+36] (2-x) = Ø 54x+72- 27x2-36x= Ø -27x2+18x+72= Ø x=-b±b2-4ac2a x=-18±182-4-27(72)2(-27)
x=-18±8100-54
x=-18±90 -54
x=
6.
72 -54
x= -4 3
1 2x+1
+ 2 + 3 =Ø (3x+5) 1-x
2x+1 1
+ 3x+5 + 1-x = Ø 2 3
(2x+1) + (2-2x+9x+15) = Ø 6 12+6+2-2x+9x+15= Ø
-2x+9x= -15-12-6-2 7x= -35 7 X=-35 7
7. 1
=
1 + 3 2x 2x+1
1
-2 3x+1 3x+2
=
2x + 2x+1 1
3
1
1
1
=
6x+2x+1 3
1
3x+1
- 3x+2
2
1
1
6x+2-3x+2 2
1
=
1
3(6x+2x+1)
1
= 18x+6x+3
1
2 (6x+2-3x+2)
1 12x+4-6x+4
=
1
24x+3
6x+8
1
24x+3
6x+8-24x+3= Ø -18x+11= Ø X= 11 -18
1=Ø 6x+8
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