Question

x^4 - 3x^3 + 6x - 4 = 0

Решить рациональное уравнение

Answer 1

$x^{4}-3x^{3}+6x-4=0\\\\(x^{4} -4)-(3x^{3}-6x)=0\\\\(x^{2}-2)(x^{2}+2)-3x(x^{2} -2)=0\\\\(x^{2}-2)(x^{2} +2-3x)=0\\\\\\\left[\begin{array}{ccc}x^{2}-2=0 \\x^{2}-3x+2=0 \end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1}=\sqrt{2} \ ; \ x_{2}=-\sqrt{2}\\x_{3}=1 \ ; \ x_{4}=2 \end{array}\right\\\\\\Otvet:\boxed{\sqrt{2} \ ; \ -\sqrt{2} \ ; \ 1 \ ; \ 2}$