Question

rozwiąż równanie :

a)x³+5x²-9x-45=0
b)x³-3x²+2x=0
c)x⁴+18x²=9x³
d)x³-5x²-25x+125=0
e)8x⁴-2x²=0
f)x³+12x²+36x=0

bardzo prosiłbym żeby ktoś to rozwiązał gdyż to jest mi potrzebne na poprawki. z Góry dziękuję.

Answer 1

a)

x^3 + 5x^2 - 9x - 45 = 0

x^2*(x+5) - 9*(x+5) = 0

(x^2 -9)(x+5) = 0

(x+3)(x-3)(x+5) = 0

 

x = -5;   v   x = -3;   v   x = 3

 

b)

x^3 - 3x^2 + 2x = 0

x(x^2 -3x +2) = 0

xo = 0

 

x^2 -3x + 2 = 0 

a = 1

b = -3

c = 2

D = b^2 - 4ac = (-3)^2 - 4 *2 = 9 - 8 = 1

VD = 1

x1 = (-b-VD)/2a = (3-1)/2 = 1

x2 = (-b+VD)/2a = (3+1)/2 = 2

 

x = 0;   v   x = 1;   v   x = 2

 

c)

x^4 + 18x^2 = 9x^3

x^4 - 9x^3 + 18x^2 = 0

x^2 *(x^2 - 9x + 18) = 0

xo = 0

 

D = 81-4*18 = 81-72 = 9

VD = 3

x1 = (9-3)/2 = 3

x2 = (9+3)/2 = 6

 

x = 0;   v   x = 3;   v x = 6

 

d)

x^3 - 5x^2 - 25 + 125 = 0

x^2 *(x-5) - 25(x-5) = 0

(x^2 - 25)(x-5) = 0

(x+5)(x-5)(x-5) = 0

 

x = -5;   v   x = 5

 

e)

8x^4 - 2x^2 = 0 

2x^2 *(4x^2 - 1) = 0

2x^2 *(2x+1)(2x-1) = 0

 xo = 0

 

2x+1 = 0

2x = -1

x = -1/2 = - 0,5

 

2x -1 = 0

2x = 1

x = 1/2 = 0,5

 

x = -0,5;   v   x = 0;   v    x = 0,5

 

f)

x^3 + 12x^2 + 36x = 0

x(x^2 + 12x + 36) = 0

xo = 0

 

x^2 + 12x + 36 = 0

D = 144 - 4 *36 = 144 - 144 = 0

x = -12/2 = -6

 

x = 0;   v   x = -6 

Answer 2

a)

 

b)

 

 

c)

 

 

d)

 

e)

 

f)