Odpowiedzi

2009-10-10T15:35:46+02:00
Zad.1
w(x)=2x⁴-x³+4x-3
P(x)=2x+3

a)3w(x)-2P(x)=3(2x⁴-x³+4x-3)-2(2x+3)=
=6x⁴-3x³+12x-9-4x-6=
=6x⁴-3x³+8x-15

b)w(x)*P(x)=(2x⁴-x³+4x-3)(2x+3)=
=4x⁵+3x⁴-2x⁴-3x³+8x²+12x-6x-9=
=4x⁵+x⁴-3x³+8x²+12x-6x-9

c)P(x)³=(2x+3)³=8x³+18x²+18x+27

Zad.2
P(x)=4ax³+6x²+2bx-4
Q(x)=4x³+2bx³+4x²-8x-4=(4+2b)x³+4x²-8x-4

4+2b=4a
2b=-8

4-8=4a
b=-4

a=-1
b=-4

Zad.3
a) (2x+4)(9-x)(x+3)=0
(2x+4)=0 (9-x)=0 (x+3)=0
x=-2 x=9 x=-3

b)(9-x²)(x²-10x+9)=0
(9-x²)=0
x=3 lub x=-3
(x²-10x+9)=0
delta=100-36=64
x₁=1 x₂=9

c)x⁴+5x³+6x²=0
x²( x²+5x+6)=0
x²=0 ( x²+5x+6)=0
x=0
x²+5x+6=0
delta= 25-21=1
x₁=-3 x₂=-2

d)(x+3)(x+8)=(x-9)(x+8)
(x+3)(x+8)-(x-9)(x+8)=0
(x+8)(x+3-x+9)=0
12(x+8)=0
x=-8

e)x³-4x²-4x+16=0
x²(x-4)-4(x-4)=0
x-4)(x²-4)=0
x=4 x=2 x=-2

f)x³-7x+6=0
x³-6x-x+6=0
x(x²-1)-6(x-1)=0
x(x-1)(x+1)-6(x-1)=0
(x-1)(x²+x-6x+6)=0
x-1=0 x²-5x+6=0
x-1=0
x=1
x²-5x+6=0
delta= 25-21=1
x₁=3 x₂=2

Zad.4
16x-x²-10xy-25y²=
=x(16-x)-5y(2x-5y)
Rząd B
Zad.1
w(x)=2x⁴-x³+4x+3
P(x)=2x-3

a)3w(x)-2P(x)=3(2x⁴-x³+4x+3)-2(2x-3)=
=6x⁴-3x³+12x+9-4x+6=
=6x⁴-3x³+8x+15

b)w(x)*P(x)=(2x⁴-x³+4x+3)(2x-3)=
=4x⁵-6x⁴-2x⁴+3x³+8x²-12x+6x+9=
=4x⁵-8x⁴+3x³+8x²-6x+9

c)P(x)³=(2x-3)³=8x³-18x²+18x-27

Zad.2
P(x)=2ax³+6x²+2bx-4
Q(x)=4x³+2bx³+6x²-8x-4=(4+2b)x³+6x²-8x-4

4+2b=2a
2b=-8

4-8=2a
b=-4

a=-2
b=4

Zad.3
a) (2x+4)(9-x)(x-3)=0
(2x+4)=0 (9-x)=0 (x-3)=0
x=-2 x=9 x=3

b)(9-x²)(x²+10x+9)=0
(9-x²)=0
x=3 lub x=-3
(x²+10x+9)=0
delta=100-36=64
x₁=-1 x₂=-9

c)x⁴-5x³+6x²=0
x²( x²-5x+6)=0
x²=0 ( x²-5x+6)=0
x=0
x²-5x+6=0
delta= 25-21=1
x₁=3 x₂=2

d)(x-3)(x+8)=(x-9)(x-3)
(x-3)(x+8)-(x-9)(x-3)=0
(x-3)(x+8-x+9)=0
17(x+8)=0
x=-8

e)x³+4x²-4x-16=0
x²(x+4)-4(x+4)=0
(x+4)(x²-4)=0
x=-4 x=2 x=-2

f)x³-7x+6=0
x³-6x-x+6=0
x(x²-1)-6(x-1)=0
x(x-1)(x+1)-6(x-1)=0
(x-1)(x²+x-6x+6)=0
x-1=0 x²-5x+6=0
x-1=0
x=1
x²-5x+6=0
delta= 25-21=1
x₁=3 x₂=2

Zad.4
16-x²-6xy-9y²=
=x(-x-6y)-(9y2-16)=
2009-10-10T16:32:01+02:00
Część B jest słabo czytelna wrzuć jako normalne zadanie , bez załacznika to rozwiążę


Zadanie1
W(x)=2x⁴-x³+4x-3 , P(x)=2x+3
a)3W(x)-2P(x)= 3*(2x⁴-x³+4x-3) - 2*(2x+3)=
6x⁴-3x³+12x-9-4x-6= 6x⁴-3x³+8x-15

b)W(x)*P(x)= (2x⁴-x³+4x-3)*(2x+3)=
4x(do 5)+6x⁴-2x⁴-3x³+8x²+12x-6x-9 =
4x(do 5) +4x⁴-3x³+8x²=6x-9

c)(P(x))³= (2x+3)³= 8x³+3*3*(2x)²+3*2x*(3)²+27= 8x³+36x²+54x+27

Zadanie 2
P(x)=4ax³+6x²+2bx-4
Q(x)=4x³+2bx³+4x²-8x-4= x³(4+2b)+4x²-8x-4

P(x)=Q(x)
4ax³+6x²+2bx-4=x³(4+2b)+4x²-8x-4
4ax³+6x²-4x²+2bx-4+4 = x³(4+2b) -8x
4ax³+2x²+2bx=x³(4+2b)-8x
Po współczynikach przy x³
4ax³= x³(4+2b)/:x³
4a = 4+2b /:4
a = 1+1/2 b
, przy x : 2bx=-8x/:2x
b=-4
wstawiamy do a
a = 1+1/2*(-4) = 1-2=-1
Zatem a =-1 , b=-4

Zadanie 3
a)(2x+4)(9-x)(x+3)=0
2x=-4, 9-x=0 , x+3 =0

x= -2 , x=9 , x=-3
b) (9-x²)(x²-10x+9)=0
(3-x)(3+x)*(x²-10x+9)=0

Wyznaczamy x₁, x₂ z r-nia
x²-10x+9=0
delta = (-10)²-4*1*9 = 100-36 =64
√delta =8
x₁=10-8/2=1
x₂=10+8/2=9

Wracamy do r-nia
(9-x²)(x²-10x=9)=(3-x)(3+x)(x-1)(x-9)

Rozwiązania : x₁ =3 , x₂=-3 , x₃=1, x₄=9

c) x⁴+5x³+6x²=0
x²(x²+5x+6)=0
x²+5x+6=0
delta =(5)²-4*1*6= 25-24 = 1
√delta =1
x₁ =-5-1/2=-3
x₂=-5+1/2=-2
Wracamy do r-nia:
x²(x+3)(x+2)=0
Rozwiązania : x₁=0 , x₂=-3, x₃=-2.

d)(x-3)(x+8)=(x-9)(x+8)
x²+8x-3x-24=x²+8x-9x-72
x²-x²+5x-x-24+72=0
4x+48=0
4x=-48/:4
x=-12
e)x³-4x²-4x+16=0
x²(x-4)-(4x -16)=0
x²(x-4)-4(x-4)=0
(x-4)(x²-4)=0
(x-4)(x-2)(x+2)=0
x₁=4 , x₂=2 , x₃=-2

f - nie mogę odczytać r-nia podobnie w zadaniu 4.





  • Użytkownik Zadane
2009-10-10T17:58:49+02:00
Zadanie1
W(x)=2x⁴-x³+4x-3 , P(x)=2x+3
a)3W(x)-2P(x)= 3*(2x⁴-x³+4x-3) - 2*(2x+3)=
6x⁴-3x³+12x-9-4x-6= 6x⁴-3x³+8x-15

b)W(x)*P(x)= (2x⁴-x³+4x-3)*(2x+3)=
4x(do 5)+6x⁴-2x⁴-3x³+8x²+12x-6x-9 =
4x(do 5) +4x⁴-3x³+8x²=6x-9

c)(P(x))³= (2x+3)³= 8x³+3*3*(2x)²+3*2x*(3)²+27= 8x³+36x²+54x+27

Zadanie 2
P(x)=4ax³+6x²+2bx-4
Q(x)=4x³+2bx³+4x²-8x-4= x³(4+2b)+4x²-8x-4

P(x)=Q(x)
4ax³+6x²+2bx-4=x³(4+2b)+4x²-8x-4
4ax³+6x²-4x²+2bx-4+4 = x³(4+2b) -8x
4ax³+2x²+2bx=x³(4+2b)-8x
Po współczynikach przy x³
4ax³= x³(4+2b)/:x³
4a = 4+2b /:4
a = 1+1/2 b
, przy x : 2bx=-8x/:2x
b=-4
wstawiamy do a
a = 1+1/2*(-4) = 1-2=-1
Zatem a =-1 , b=-4

Zadanie 3
a)(2x+4)(9-x)(x+3)=0
2x=-4, 9-x=0 , x+3 =0

x= -2 , x=9 , x=-3
b) (9-x²)(x²-10x+9)=0
(3-x)(3+x)*(x²-10x+9)=0

Wyznaczamy x₁, x₂ z r-nia
x²-10x+9=0
delta = (-10)²-4*1*9 = 100-36 =64
√delta =8
x₁=10-8/2=1
x₂=10+8/2=9

Wracamy do r-nia
(9-x²)(x²-10x=9)=(3-x)(3+x)(x-1)(x-9)

Rozwiązania : x₁ =3 , x₂=-3 , x₃=1, x₄=9

c) x⁴+5x³+6x²=0
x²(x²+5x+6)=0
x²+5x+6=0
delta =(5)²-4*1*6= 25-24 = 1
√delta =1
x₁ =-5-1/2=-3
x₂=-5+1/2=-2
Wracamy do r-nia:
x²(x+3)(x+2)=0
Rozwiązania : x₁=0 , x₂=-3, x₃=-2.

d)(x-3)(x+8)=(x-9)(x+8)
x²+8x-3x-24=x²+8x-9x-72
x²-x²+5x-x-24+72=0
4x+48=0
4x=-48/:4
x=-12
e)x³-4x²-4x+16=0
x²(x-4)-(4x -16)=0
x²(x-4)-4(x-4)=0
(x-4)(x²-4)=0
(x-4)(x-2)(x+2)=0
x₁=4 , x₂=2 , x₃=-2