Question

Найти действительные корни уравнения x⁵ - 2x⁴ - 3x³ + 6x² - 4x + 8 = 0

Answer 1

$\displaystyle x^5-2x^4-3x^3+6x^2-4x+8=0\\\\x^4(x-2)-3x^2(x-2)-4(x-2)=0\\\\(x-2)(x^4-3x^2-4)=0\\\\x-2=0 ; x^4-3x^2-4=0$

$\displaystyle x-2=0; x=2$

$\displaystyle x^4-3x^2-4=0\\\\D=9+16=25=5^2\\\\x^2= \frac{3\pm 5}{2}\\\\x^2=4; x^2=-1\\\\x^2=4; x=\pm 2\\\\ x^2 \neq -1$

Ответ х=2 или х=-2