Question

Rezolvați ecuatia": x^4-4x^3+x^2+8x-6=0

Answer 1

[tex]x^4-4x^3+x^2+8x-6=0\\ x^4-x^3-3x^2-2x^2+2x+6x-6=0\\ x^3(x-1)-3x^2(x-1)-2x(x-1)+6(x-1)=0\\ (x-1)(x^3-3x^2-2x+6)=0\\ (x-1)[x^2(x-3)-2(x-3)]=0\\ (x-1)(x-3)(x^2-2)=0\\ x-1=0; x_1=1\\ x-3=0; x_2=3\\ x^2-2=0; x^2=2; x_3=\sqrt{2}, x_4=-\sqrt{2}[/tex]