Risolvi y=(x^2+3x+2)^2

$$y = ( x ^ { 2 } + 3 x + 2 ) ^ { 2 }$$

Trova y

$$y=\left(\left(x+1\right)\left(x+2\right)\right)^{2}$$

Procedura della soluzione

Eleva x^{2}+3x+2 al quadrato.

$$y=x^{4}+6x^{3}+13x^{2}+12x+4$$

Trova x (soluzione complessa)

$$x=\frac{-\sqrt{4\sqrt{y}+1}-3}{2}$$

$$x=\frac{\sqrt{4\sqrt{y}+1}-3}{2}$$

$$x=\frac{\sqrt{-4\sqrt{y}+1}-3}{2}$$

$$x=\frac{-\sqrt{-4\sqrt{y}+1}-3}{2}$$

Trova x

$$\left\{\begin{matrix}x=\frac{-\sqrt{4\sqrt{y}+1}-3}{2}\text{; }x=\frac{\sqrt{4\sqrt{y}+1}-3}{2}\text{, }&y\geq 0\\x=\frac{-\sqrt{-4\sqrt{y}+1}-3}{2}\text{; }x=\frac{\sqrt{-4\sqrt{y}+1}-3}{2}\text{, }&y\geq 0\text{ and }y\leq \frac{1}{16}\end{matrix}\right,$$