Answer:
A. x = 0, x = -3, x = 2, and x = -2
Step-by-step explanation:
[tex]x^{4} +12x=4x^{2} +3x^{3}[/tex]
by moving the terms on the left side to the right side
[tex]x^{4} -3x^{3} -4x^{2} +12x = 0[/tex]
factor an [tex]x^{3}[/tex] from [tex]x^{4} -3x^{3}[/tex]
and factor - 4[tex]x[/tex] from [tex]-4x^{2} +12x[/tex]
the equation becomes :
[tex]x^{3} (x - 3 )-4x (x - 3)[/tex] = 0
take [tex](x - 3)[/tex] as a common factor the equation becomes :
[tex](x-3)(x^{3}-4x )[/tex] = 0
thus
[tex]x - 3 = 0[/tex]⇒[tex]x = 3[/tex]
and
[tex]x^{3} - 4x = 0[/tex] by factoring an x we get :
[tex]x(x^{2}-4 ) =0[/tex] ⇒ [tex]x[/tex] = 0 and [tex]x^{2} - 4 = 0[/tex]
[tex]x^{2} - 4 =0[/tex]⇒[tex]x = 2[/tex] and [tex]x = -2[/tex]
Thus
the values are :
x = 0, x = -3, x = 2, and x = -2
