Soluciones a las actividades de cada epígrafe

5
Soluciones a las actividades de cada epígrafe
PÁGINA 100
Pág. 1
3 Resuelve las siguientes ecuaciones:
a) (3x + 4)(5x – 7) = (2x + 7)2 + 53
2
b) x – 3x + 2 = x + 12
2
6
2
c) (x + 1) – 3(x – 1) + 3x (x + 1) = 3
2
4
2
2
2
d) 3x (x + 1) – (x – 2) = (x + 1)(x – 1) + 15
2
a) (3x + 4)(5x – 7) = (2x + 7)2 + 53
15x 2 – 21x + 20x – 28 = 4x 2 + 28x + 49 + 53
15x 2 – 4x 2 – 21x + 20x – 28x – 28 – 49 – 53 = 0
11x 2 – 29x – 130 = 0
x = 29 ± √841 – 4 · 11 · (–130) = 29 ± √841 – 5 720 = 29 ± √6 561 =
22
22
22
= 29 ± 81 8 x1 = 5 y x2 = –52 = –26
22
22
11
2
b) x – 3x + 2 = x + 12
2
6
3(x 2 – 3x) + 12 = x + 12
3x 2 – 9x + 12 – x – 12 = 0
3x 2 – 10x = 0 8 x (3x – 10) = 0 8 x1 = 0 y x2 = 10
3
2
c) (x + 1) – 3(x – 1) + 3x (x + 1) = 3
2
4
2
2
2
2(x + 1) – 3(x – 1) + 6x (x + 1) = 6
2(x 2 + 2x + 1) – 3x + 3 + 6x 2 + 6x = 6
2x 2 + 4x + 2 – 3x + 3 + 6x 2 + 6x – 6 = 0
8x 2 + 7x – 1 = 0
x = –7 ± √49 – 4 · 8 · (–1) = –7 ± √81 = –7 ± 9 8 x1 = 1 y x2 = –1
16
8
16
16
2
d) 3x (x + 1) – (x – 2) = (x + 1)(x – 1) + 15
2
2
3x 2 + 3x – (x – 2) = x 2 – x + x – 1 + 15
2
6x 2 + 6x – x 2 + 4x – 4 = 2x 2 – 2x + 2x – 2 + 30
3x 2 + 10x – 32 = 0
x = –10 ± √100 – 4 · 3 · (–32) = –10 ± √484 = –10 ± 22 8
6
6
6
8 x1 = 2 y x2 = –32 = –16
6
3
Unidad 5. Ecuaciones