MATERIAL DIDACTICO MATEMATICA I 1


NUMEROS REALES

1. ECUACIONES
1.1. Ecuaciones Lineales
1.
Resolver:
5x – 11 = 3x + 17
Rpta:
x = 14
2.
Resolver:
x – (2x + 1) = 8 – (3 x + 3)
Rpta:
x = 3
3.
Resolver:
5x – [4x – 3(2 – 7x)] = 3x – (11 – 2x)
Rpta:

4.
Resolver:
3x – 4(6 – x) = 15 – 6x
Rpta:
x = 3
5.
Resolver:
2(3x + 3) – 4(5x – 3) = x(x – 3) – x(x + 5)
Rpta:
x = 3
6.
Resolver:
2x + (x + 2)(x – 4) = x(x + 4)
Rpta:
x = –2
7.Resolver:
(3 x + 2)2 – 2x – (3x – 12) = 9(x2 – 4) – 3 x – 4
Rpta:
x = –
8.
Resolver:
14 – (5x – l)(2 x + 3) = 17 – (10x + 1)(x – 6)
Rpta:
x = –
9.
Resolver:

Rpta:
x = 3
10.
Resolver:

Rpta:
x ∈ ℝ
11.
Resolver:

Rpta:
x ∈ Ø
12.
Resolver:

Rpta:
x ∈ ℝ
13.
Resolver:

Rpta:
x =
14.
Resolver:

Rpta:
x =
15.
Resolver:

Rpta:
x =
16.
Resolver:

Rpta:
x =
17.
Resolver:

Rpta:
x = 8
18.
Resolver:Rpta:
x ∈ Ø
19.
Resolver:

Rpta:
x = 12
20.
Resolver:

Rpta:
x ∈ Ø
21.
Resolver:

Rpta:
x = – 7
22.
Resolver:

Rpta:
x = 8
23.
Resolver:

Rpta:
x =
24.
Resolver:

Rpta:
x = 14
25.
Resolver:

Rpta:
x = 9
26.
Resolver:

Rpta:
x =
27.
Resolver:

Rpta:
x =
28.
Resolver:

Rpta:
x = – 4
29.
Resolver:

Rpta:
x = –16
30.
Resolver:

Rpta:
x =106
31.
Resolver:

Rpta:
x = 108

1.2 Ecuaciones Cuadráticas1.
Resolver:
x 2 – 13 = 12
Rpta: C.S. =
{–5,5}
2.
Resolver:
3 x 2 – 4 = 28 + x2
Rpta: C.S. =
{–4,4}
3.
Resolver:
3(x2 – 11) + 2(x 2 – 7) = 38
Rpta: C.S. =
{– ,}
4.
Resolver:
4x 2 + 20 = 4
Rpta: C.S. =
Ø
5.
Resolver:
4x 2 – 3x = 0
Rpta: C.S. =

6.
Resolver:
2x 2 – 10x = 0
Rpta: C.S. =
{0,5}
7.
Resolver:
x2 + x + 24 = 0
Rpta: C.S. =
{–8, –3}
8.
Resolver:
x2 + 19 x + 84 = 0
Rpta: C.S. =
{–12, –7}9.
Resolver:
2x 2 + 13x + 6 = 0
Rpta: C.S. =

10.
Resolver:
4x 2 – 42x = 7 x – 12
Rpta: C.S. =

11.
Resolver:
x(x – 3) = 2(x + 7)
Rpta: C.S. =
{–2, 7}
12.
Resolver:
2x(x + 3) = 7(x + 4)
Rpta: C.S. =

13.
Resolver:
x 2 + 10 x + 1 = 0
Rpta: C.S. =
{2 – 5, –2 – 5}
14.
Resolver:
x2 – 6x + 1 = 0
Rpta: C.S. =
{3 – 2,3 + 2}
15.
Resolver:
5x2 – 8x + 2 = 0
Rpta: C.S. =

16.
Resolver:
3 x 2 – 6x + 5 = 0
Rpta:C.S. =
Ø
17.
Resolver:
2 x 2 – 12 x + 4 = 0
Rpta: C.S. =
{3 – , 3 + }
18.
Resolver:
3 x 2 – 8 x + 1 = 0
Rpta: C.S. =

19.
Resolver:
x2 + 10x – 9 = 0
Rpta: C.S. =
{–5 – , –5 + }
20.
Resolver:
x(x – 1) = 0
Rpta: C.S. =

21.
Resolver:
10(x + 2) – 19 = (1 + 5x)(1 – 5x)
Rpta: C.S. =

22.
Resolver:

Rpta: C.S. =
Ø
23.
Resolver:

Rpta: C.S. =


1.3. Propiedades de las raíces de las ecuacionescuadráticas
Hallar la suma y el producto de las raíces de las siguientes ecuaciones cuadráticas:
1.
2x2 – 3x + 4 = 0
Rpta: S = , P = 2
2.
3x2 – 3x + 2 = 0
Rpta: S = l , P =
3.
5x2 + x – 2 = 0
Rpta: S = , P =
4.
– x2 + 2x – 3 = 0ººººº
Rpta: S = 2, P = 3
5.
x2 – 3 x + 6 = 0
Rpta: S = 3, P = 6
6.
2x2 – 3 x + 9 = 0
Rpta: S = , P =
Formas las ecuaciones cuadráticas, cuyas raíces se dan a continuación:7.
x1 = 5, x2 = –3
Rpta:
x2 – 2x – 15 = 0
8.
xl = 3, x2 = 1
Rpta:
x2 – 4x + 3 = 0
9.
x1 = , x2 =
Rpta:

10.
x1 = , x2 =
Rpta:

11.
x1 = , x2 = 5
Rpta:

12.
xl = 3+ , x2 = 3 –
Rpta:
x2 – 6x + 7 = 0

Hallar el valor de k para que:
13. Una raíz sea –2 en la ecuación: (k2 – 3)x2 – 3(k – l)x – 5k = 0.
Rpta: C.S. =
14. El producto de las raíces sea 6 en la ecuación: (k + 2)x2 – 5x + 2k = 0.Rpta: S = {–3}
15. Las dos raíces sean iguales en la ecuación: x2 + kx = k – 8.
Rpta: C.S. = {–8,4}
16. Las dos raíces sean iguales en la ecuación: (k + 4)x2 – 1 = (2k + 2)x – k.
Rpta: C.S. = {5}
17. Las dos raíces sean números recíprocos en la ecuación: {k + 2)x2 + 10x + 3k = 0.
1 Rpta: C.S. = {1}
18. Una raíz sea el doble de la otra en la ecuación: 2x2 – 4x + k2 – 3 = 0.
Rpta: C.S. =19. Las dos raíces sean iguales en la ecuación: (k – 1)x2 – 5x + 3k –7 = 0.
Rpta: C.S. =




1.4. Ecuaciones réductibles a cuadráticas
1.
Resolver:

Rpta: C.S. =
{–3, –1, 2, 6}
2.
Resolver:

Rpta: C.S. =
{–2, 2, –3, 3}
3.
Resolver:

Rpta: C.S. =
{1, –3, 3 ± 2}
4.
Resolver:
(x2 + 3x + 2) 2 – 8 (x2 + 3x) = 4
Rpta: C.S. =
{0, –3, 1, –4}
5.
Resolver:

Rpta: C.S. =
{–6, –2, 1, 3}
6.
Resolver:...