9.

[2+x ]=-[x]²+4

[x]²+ [2+x ]=4

Puntos críticos

X=0

2+x=0

X=-2

[ a ] + [ b ] puntos críticos donde se iguala a cero

2 1
8 3
- -2 0
X < -2 -2 < x < 0 x > 0ç

❶X=1 ❷ x=1

[ x ] ²+[ 2+x ] = 4 - [ x ]²+( 2 + x ] = 4

x² + x + 2 – 4 = 0 - x² + 2 + x = 4

x² + x – 2 = 0 0 = x² - x – 2 + 4
x +2 2x 0 = x² - x + 2
−x
x -1 formula general
x

(x+2) (x-1) = 0 a= 1
X = -2 ^ x = 1 b= -1
C= 2
−1 .−1 ± √ 12−4 .1(2)
❸ x = -3 x=
2 .1
−1.−1 ± √ 1−4.1 .2
- [ x ]²+( 2 + x ] = 4 x=
21
−1.−1 ± √1−8
- x² + 2 - x = 4 x=
2.1
−1.−1 ± √ 7
0 = x² + x + 4 + 2 x=
2 .1
−1.−1 ± √ 7
0 = x² + x + 6 x=
2
1± √ 7
formula general x=
2
a= 1 La factorización en primos de −7 es i√ 7
b= 3 √−1 .7=i √ 7
c= 6 factores primos
−1 ± √ 1 −4 .1(6) 2
x= i √ 7=i √ 7
2 .1
−1 ± √ 1−24 x=
1± i √ 7
x=
2 .1 2
−1 ± √−23 x 1=
1+i √ 7
x=
2 2
 −1i √ 7
Factor primo de -23 es i √ 23 x 2=
2
√ ❑−23=√ −1.23
Factores primos

i √ 23=i √ 23
−1 ±i √ 23
x=
2
−1+i √ 23
x 1=
2
−1−i √23
x10.
2= [ x – 3 ] [ x + 5 ] + x = 2
2
[x–3][x+5]=2–x
[ (x – 3) (x + 5) ] 2 – x
[ 6x² + 5x – 3x – 15 ] = 2 – x
[ x² + 2x – 15 ] = 2 – x

[a ]=a ^ [ a ] = -a

x² + 2x – 15 = 2 – x x² + 2x – 15 = - (2 – x)

x² + 3x – 17 = 0 x² + 2x – 15 = - 2 + x

formula general x² + x – 13 = 0

a= 1 formula general

b= 3 a= 1

c= - 17 b= 1

−3 ± √ 32−4 .1(−17)
x= c= -13
2 .1

−3 ± √ 9+68 −1 ± √ 12−4 .1(−13)

−3 ± √ 77 −1 ± √ 1+52
x¿ x=
2 .1 2.1
−3 ± √ 77 −1 ± √ 53
x¿ x=
2 2 .1
−1 √53
separa x=
2
−3+ √ 77
x¿ separa
2
 −3−√ 77 −1+ √ 53
x¿ x=
2 2

x1¿ √
77−3 −1−√ 53
x=
2 2

x2= √ √53−1
− 77−3 − √53−1
x 1= x 2=
2 2 2