a)
[tex]-x^{3} = 27\\\\-x^{3} = 3^{3}\\\\-x = 3 \ \ /:(-1)\\\\\boxed{x = -3}[/tex]
b)
[tex]-x^{2} = -2x\\\\-x^{2}+2x = 0 \ \ /\cdot(-1)\\\\x^{2}-2x = 0\\\\x(x-2) = 0\\\\x = 0 \ \vee \ x-2 = 0\\\\\boxed{x = 0 \ \vee \ x = 2}[/tex]
c)
[tex]2x^{2} = 8 \ \ /:2\\\\x^{2} = 4\\\\x^{2}-4 = 0\\\\(x+2)(x-2) = 0\\\\x+2 = 0 \ \vee \ x-2 = 0\\\\\boxed{x = -2 \ \vee \ x = 2}[/tex]
d)
[tex]x^{2}(c-9) = 0\\\\x^{2} = 0 \ \vee \ x-9 = 0\\\\x = 0 \ \vee \ x = 9 \ \ \ (brak \ 9)[/tex]
e)
[tex]\frac{x+1}{3} = -\frac{1}{3} \ \ /\cdot3\\\\x+1 = -1\\\\x = -1-1\\\\\boxed{x = -2}[/tex]
f)
[tex]\frac{x(x+2)}{5} = -\frac{4}{5} \ \ /\cdot 5\\\\x(x+2) = -4\\\\x^{2}+2x+4 =0\\\\(x+2)^{2} = 0\\\\x+2 = 0\\\\\boxed{x = -2}[/tex]
g)
[tex]x^{2}+2 = 0\\\\x^{2} = -2, \ sprzecznosc, \ brak \ rozwiazania[/tex]
h)
[tex]x(x+2) = x^{2}+2x\\\\x^{2}+2x = x^{2}+2x\\\\x^{2}-x^{2}+2x-2x = 0\\\\0 = 0[/tex]
równanie tożsamościowe, nieskończenie wiele rozwiązań
Odp. Poza d), g) i h).
