Question

Помогите, пожалуйста, решить уравнение.
x⁴+8x³+27x²+44x+22=0​

Answer 1

$\displaystyle x^4+8x^3+27x^2+44x+22=0\\x^4+8x^3+16x^2-16x^2+27x^2+44x+22=0\\x^4+8x^3+16x^2+11x^2+44x+22=0\\(x^2+4x)^2+11(x^2+4x)+22=0\\x^2+4x=a\\a^2+11a+22=0\\a_{1,2}=\frac{-11\pm\sqrt{121-88}}{2}=\frac{-11\pm\sqrt{33}}{2}\\a_1=\frac{-11+\sqrt{33}}{2};a_2=\frac{-11-\sqrt{33}}{2}\\x^2+4x+\frac{11-\sqrt{33}}{2}=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2+4x+\frac{11+\sqrt{33}}{2}=0\\x_{1,2}=-2\pm\sqrt{(4-\frac{11-\sqrt{33}}{2})_{>0}}\ \ \ \ x_{1,2}=-2\pm\sqrt{(4-\frac{11+\sqrt{33}}{2})_{<0}}$

$\displaystyle x_1=-2+\sqrt{4-\frac{11-\sqrt{33}}{2}}\ \ \ \ \ \ \ \ \ \ \ x\in\varnothing\\x_2=-2-\sqrt{4-\frac{11-\sqrt{33}}{2}}$