taller de repaso 5

TALLER 5

NIVEL 1
1.
A) 〖2X〗^2+2X-1X+1=X^2+7X-X-7
2X^2+X+1=X^2+6X-7
2X^2-X^2-6X+X=-7-1
X^2-5X=-8
X^2-5X+8=0
a=1 b=-5 c=8
x=(-(-5)±√(〖-5〗^2-4(1)(8) ))/2
x=(5±√(25+32))/2
x=(5±√57)/2
x=(5+7.54)/2 x=(5-7.54)/2
x=12.54/2 x=-2.242
x=6.3 x=-1.12

B) 2X^2+2(2X)(3)+3^2=X-3X^(2 )
2X^2+12X+9=X-3X^2
2X^2+3X^2+12X-X=-9
5X^2+11X+9=0
a= 5 b=11 c=9
x=((-11±√(〖11〗^2+4(5)(9))))/10
x=(-11±√(121+180))/10
x=(-11±√301)/10
x=((-11±17.3))/10
x=((-11+17.3))/10 x=(-11-17.3)/10
x=6.3/10 x=-28.3/10
x=0.63 x=-0.3

2.
A) 4X^2-20X+25=0 a=4 b=-20 c=25
X=(-(-20)±√((-2〖0)〗^2+4(4)(25)))/8
X=(20±√(400+400))/8
X=(20±√800)/8
X=(20+28.3)/8 X=((20-28.3))/8
X=48.3/8=6.03 X=8.3/8=1.03

B) 0.5X^2-2X-6=0 a=0.5 b=-2 c=-6
X=(-(-2)±√((-2)^2+4(0.5)(-6) ) )/1
X=2±√(4-12 )
X=2±√(-8)
X=2+√8 i=2+2.8 i=4.8 i X=2-√8 i=2-2.8 i= -0.8i



C)3X^2-6X-12
X=(-(-6)±√((-6)^2+4(3)(-12) ))/6
X=(6±√(36-144))/6
X=(6±√(-108) ))/6
X=(6±√(108 ) i
X=(6+10.4 i)/6 X=((6-10.4 i))/6
X=(16.4 i)/6 X=4.4i/6
X=2.7 i X=0.7 i
4.
a(〖3)〗^2+b(3)-1=0
a=9a+3b-1=0
a=(-3b-1)/9
(-3b-1)/9 〖 3〗^(2 )+3b-1=0
(-3b-1)(9)+3b-1=0
-24b-9-1=0
-24b=10
b=10/(-24)
b=-0.41
a=(-3(-0.41)-1)/9
a=(1.23-1)/9
a=0.23/9
a=0.02

6. X ↦ numero natural
x=12-x^2
x^2+x+12=0
x=(-1±√(1^2+4(1)(12) ))/2
x=(-1±√(1+48))/2
x=(-1± √(49 ))/2
x=(-1±7)/2
x=(-1+7)/2 x=(-1-7)/2
x=6/2=3 x=-8/2=-4
PRUEBA
3=12-(〖3)〗^(2 )
3=12-9
3=3

7.x-(-x)=9/20
x+x=0.4
x=0.4/2
x=0.2
PRUEBA
0.2—0.2=0.4
0.4=0.4
9. X ↦ NUMERO ENTERO
X+1 NÚMERO CONSECUTIVO
X^2+(X+1)^2=61
X^2+X^(2 ) +1=61
X^2+X^(2 )=61-1
2X^2=60
X^(2 )=60/2
X^2=30
√(X^2 )=√30
X^(2 )=5.4 APROXIMA A 5
5.4+1=6.4 APROXIMA A 6
PRUEBA
5^2+ 6^(2 )=25+36=61

10) X ↦ NUMERO 1
X+1↦ NUMERO CONSECUTIVO
x(x+1)=272
x^(2 )+x=272
x=((-(1)±√(1^2+4(1)(272) )))/2
x=( -1±√(1+1088))/2
x=(-1±√(1089 ))/2
x=(-1 ±33)/2
x=(-1+33 )/2
x=32/2
x= 16
x+1=otro numero 16+1=17
PRUEBA
16*17=272

14.
A) x^2-6x+7=(x-1)(x+7) V
x-1=0
x=1
x+7=0
x=-7
B)
(x-3)^(2 )-2=0 V
〖(x〗^2-2(x)(3)+3^2)-2=0
x^2-6x+9-2 =0
x^(2 )-6x+7=0 Es igual a la ecuación inicial
C)
(x+1)(x+7)=0 F
x^(2 )-3^2-2=0
x^2+7x+x+7=0
x^2+8x+7=0
D)
(x+1)(x-7)=0 F
x^2 -7x+x-7=0
x^2-6x-7=0



E)
(x-1)(x-7)=0 F
x^2-7x-x+7=0
x^(2 )-8x+7=0
F)
(x+7)(x+1)
x^2+x+7x+7
x^2+8x+7
15.
A)
(x-12) porque (x+1)(x-12)=
x^2-12x+x-12 =
x^2-11x-12
B)
x+1=0
x=-1
x-12
x=12
NIVEL 2
1.
A)1+2X=6/X
(1+2X)X=6
X+2X^2=6
2X^2+X-6=0
(2X+3) (X-2)
2X=-3
X=-3/2
(X-2)=0
X=2

REFLEXION
con este taller aprendemos varias operaciones a darle las pruebas a ellas
y comprovar que son ciertas muy interesante