Odpowiedź:
Zad. 1
a) [tex]x^{2} - 9 = 0[/tex]
[tex]x^{2} = 9\\x = + 3\\x = - 3\\x = 3\\x_{1} = - 3, x_{2} = 3[/tex]
b) 16 - 4[tex]x^{2}[/tex] = 0
[tex]4 - x^{2} = 0\\-x^{2} = - 4\\x^{2} = 4\\x = + \\x = - 2\\x = 2\\x_{1} = -2 , x_{2} = 2[/tex]
Zad. 2
a) 4 [tex]x^{2}[/tex] - 8x = 0
4x * (x - 2) = 0
x * (x - 2 ) = 0
x = 0
x-2 = 0
[tex]x_{1} = 0 , x_{2} = 2[/tex]
b) 3x + 12 [tex]x^{2}[/tex] = 0
3x * (1+ 4x ) = 0
x * ( 1+ 4x) = 0
x = 0
x + 4x = 0
x = 0
x = - [tex]\frac{1}{4}[/tex]
[tex]x_{1} = -\frac{1}{4} , x_{2} = 0[/tex]
Zad. 3
a) ( x - 3 )(2x + 60) = 0
x - 3 = 0
2x + 60 = 0
x = 3
x = - 30
[tex]x_{1} = - 30 , x_{2} = 3[/tex]
b ) - 2x (x-5) = 0
2x * (x - 5 ) = 0
x * ( x - 5) = 0
x = 0
x - 5 = 0
x = 0
x = 5
[tex]x_{1} = 0 , x_{2} = 5[/tex]
Zad. 4
[tex]- x^{2} + 4x + 21 = 0\\x^{2} - 4x - 21 = 0\\x^{2} + 3x - 7x - 21 = 0\\x * ( x + 3 ) - 7 ( x + 3 ) = 0\\( x + 3) * ( x - 7 ) = 0\\x + 3 = 0\\x - 7 = 0\\x = -3\\x = 7\\x_{1} = - 3, x_{ 2} = 7[/tex]
Zad 5
(x + 1) (2x - 3) = 3x( x + 1 )
[tex]2 x^{2} - 3 x + 2 x - 3 = 3 x^{2} + 3 x\\ 2 x^{2} - x - 3 - 3x^{2} - 3x =0\\ - x^{2} - 4 x - 3 = 0\\x^{2} + 4 x + 3 = 0\\x *( x + 3 ) + x + 3 = 0\\( x + 3 ) * ( x + 1 ) = 0\\ x+ 3 = 0\\x + 1 = 0\\x_{1} = - 3 , x_{2} = -1[/tex]
