1) $$ x^{3}+5 x^{2}-16 x-8 $$ 2) $$ x^{3}+8 x^{2}=x+8 $$

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Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x^{3}+8x^{2}-x-8=0$$
- step1: Factor the expression:
  $$\left(x-1ight)\left(x+1ight)\left(x+8ight)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-1=0\&x+1=0\&x+8=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=1\&x=-1\&x=-8\end{align}$$
- step4: Rewrite:
  $$x_{1}=-8,x_{2}=-1,x_{3}=1$$
Solve the equation $$ x^{3}+5 x^{2}-16 x-8=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x^{3}+5x^{2}-16x-8=0$$
- step1: Calculate:
  $$\begin{align}&x\approx -7.095932\&x\approx -0.443892\&x\approx 2.539824\end{align}$$
- step2: Rewrite:
  $$x_{1}\approx -7.095932,x_{2}\approx -0.443892,x_{3}\approx 2.539824$$
Решим оба уравнения по очереди.

1) Для уравнения $$ x^{3}+5 x^{2}-16 x-8=0 $$ мы получили следующие корни:
   - $$ x_{1} \approx -7.095932 $$
   - $$ x_{2} \approx -0.443892 $$
   - $$ x_{3} \approx 2.539824 $$

2) Для уравнения $$ x^{3}+8 x^{2}-x-8=0 $$ корни следующие:
   - $$ x_{1} = -8 $$
   - $$ x_{2} = -1 $$
   - $$ x_{3} = 1 $$

Таким образом, у нас есть три корня для первого уравнения и три корня для второго уравнения.
Корни уравнения $$ x^{3}+5 x^{2}-16 x-8=0 $$: - $$ x \approx -7.095932 $$ - $$ x \approx -0.443892 $$ - $$ x \approx 2.539824 $$ Корни уравнения $$ x^{3}+8 x^{2}-x-8=0 $$: - $$ x = -8 $$ - $$ x = -1 $$ - $$ x = 1 $$

1) \( x^{3}+5 x^{2}-16 x-8 \) 2) \( x^{3}+8 x^{2}=x+8 \)

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