1)
(x-3)(x+2)x = 0
x-3=0 ∨ x+2=0 ∨ x=0
x=3 ∨ x=-2 ∨ x=0
x ∈ {-2;0;3}
2)
[tex]x^4-1=0\\(x^2-1)(x^2+1)=0\\x^2=1, x^2=-1[/tex]
x = 1 ∨ x = -1 ∨ [tex]x^2=-1[/tex] (sprzeczność, [tex]x^2[/tex]≥0)
x ∈{-1;1}
3)
[tex]x^3+4x^2-2x-8=0\\x^2(x+4) -2(x+4)=0\\(x^2-2)(x+4)=0[/tex]
[tex]x^2=2[/tex] ∨ x = -4
x = 2 ∨ x = -2 ∨ x = -4
x ∈{-4;-2;2}
4)
[tex]x^3+3x+4=0\\x^3-x + 4x + 4=0\\x(x^2-1) + 4(x+1) = 0\\x(x-1)(x+1) + 4(x+1)=0\\(x+1)(x(x-1)+4)=0\\[/tex]
x = -1 ∨ [tex]x(x-1)+4=0[/tex]
[tex]x^2-x+4=0\\[/tex]
Δ = [tex]1 -4*4 < 0[/tex], zatem równanie [tex]x^2-x+4=0\\[/tex] nie ma rozwiązań.
x ∈ {-1}
5)
[tex]4x^4-81=0\\(2x^2-9)(2x^2+9)=0[/tex]
[tex]2x^2=9[/tex] ∨ [tex]2x^2 = -9[/tex] (sprzeczność, [tex]x^2\geq 0[/tex])
[tex]2x^2=9\\x^2 = \frac{9}{2} \\x_1 = \frac{3}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{3\sqrt{2} }{2} \\x_2 = -\frac{3\sqrt{2} }{2}[/tex]
x ∈ {[tex]{-\frac{3\sqrt{2} }{2}, \frac{3\sqrt{2} }{2}}[/tex]}
