Question

rozwiąż równania:

a)-4x(x-3)(x-)(x+4)=0

b)(x-1-)(x-1+)(x-4)=0

c)(=0

d)(x+4)-(x+4)=0

e)(-4)-49(-4)=0

f)(x-)-2(x-)=0

Answer 1

a)

- 4x( x - 3)*( x - p(2))*(x + 4) = 0

x = 0  lub x -3 = 0  lub x - p(2) = 0 lub x + 4 = 0

x = 0  lub  x = 3     lub  x = p(2)   lub  x = - 4

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b)

( x - 1 -p(2))*( x - 1 + p(2))*( x - 4) = 0

x - 1 - p(2) = 0   lub  x - 1 + p(2) = 0   lub  x - 4 = 0

x = 1 = p(2)       lub   x = 1 - p(2)     lub  x = 4

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c)

6x^2 *(x + 2)^4  * ( x - 3)^3 = 0

x = 0  lub x + 2 = 0  lub  x - 3 = 0

x = 0   lub  x = -2  lub  x = 3

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d)

4 x^2( x + 4) - ( x + 4) = 0

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

x + 4 = 0   lub  4 x^2 - 1 = 0

x = - 4      lub  4 x^2 = 1

x = - 4      lub     x^2 = 1/4

x = - 4      lub   x = -1/2  lub  x = 1/2

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e)

9 x^2 *( x^2 - 4)- 49*( x^2 - 4) = 0

( x^2 - 4)*(x^2 - 49) = 0

( x - 2)*(x + 2)*( x - 7)*( x + 7) = 0

x -2 = 0   lub  x + 2 = 0  lub  x - 7  = 0  lub  x + 7  = 0

x = 2  lub  x = - 2   lub  x = 7  lub  x = - 7

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f)

x^2 *( x - p(2))- 2 *( x - p(2)) = 0

( x - p(2))*( x^2 - 2) = 0

( x - p(2))*( x - p(2))*( x + p(2)) = 0

x -p(2) = 0  lub  x + p(2) = 0

x = p(2)    lub  x = - p(2)

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p(2)  - pierwiastek kwadratowy  z  2