(x+2)*((x+2)*(x^2+2)+2)+8еслиx=-1 (упростите выражение)

Вы ввели

        /        / 2    \    \    
(x + 2)*\(x + 2)*\x  + 2/ + 2/ + 8

$$\left(x + 2\right) \left(\left(x + 2\right) \left(x^{2} + 2\right) + 2\right) + 8$$

Подстановка условия

(x + 2)*((x + 2)*(x^2 + 2) + 2) + 8 при x = -1

подставляем

        /        / 2    \    \    
(x + 2)*\(x + 2)*\x  + 2/ + 2/ + 8

$$\left(x + 2\right) \left(\left(x + 2\right) \left(x^{2} + 2\right) + 2\right) + 8$$

            /            /     2\\
8 + (2 + x)*\2 + (2 + x)*\2 + x //

$$\left(x + 2\right) \left(\left(x + 2\right) \left(x^{2} + 2\right) + 2\right) + 8$$

переменные

x = -1

$$x = -1$$

               /               /        2\\
8 + (2 + (-1))*\2 + (2 + (-1))*\2 + (-1) //

$$\left((-1) + 2\right) \left(\left((-1) + 2\right) \left((-1)^{2} + 2\right) + 2\right) + 8$$

            /            /        2\\
8 + (2 - 1)*\2 + (2 - 1)*\2 + (-1) //

$$\left(-1 + 2\right) \left(2 + \left(-1 + 2\right) \left(\left(-1\right)^{2} + 2\right)\right) + 8$$

13

$$13$$

Численный ответ

8.0 + (2.0 + x)*(2.0 + (2.0 + x)*(2.0 + x^2))

Рациональный знаменатель

      4      3      2       
20 + x  + 4*x  + 6*x  + 10*x

$$x^{4} + 4 x^{3} + 6 x^{2} + 10 x + 20$$

Общий знаменатель

      4      3      2       
20 + x  + 4*x  + 6*x  + 10*x

$$x^{4} + 4 x^{3} + 6 x^{2} + 10 x + 20$$

Комбинаторика

      4      3      2       
20 + x  + 4*x  + 6*x  + 10*x

$$x^{4} + 4 x^{3} + 6 x^{2} + 10 x + 20$$

Разложение на множители

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$$\left(x + \left(1 + \frac{\sqrt{- 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}} - \frac{12}{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}} - \frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}}{2} - \frac{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}{2}\right)\right) 1 \left(x + \left(1 + \frac{\sqrt{- 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}} + \frac{12}{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}} - \frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}}{2} + \frac{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}{2}\right)\right) \left(x - \left(-1 + \frac{\sqrt{- 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}} - \frac{12}{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}} - \frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}}{2} + \frac{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}{2}\right)\right) \left(x + \left(1 + \frac{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}} + \frac{12}{\sqrt{\frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}} + 2 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}} - \frac{26}{3 \sqrt[3]{\frac{9}{4} + \frac{\sqrt{98895} i}{36}}}}}{2}\right)\right)$$