Решите уравнение: 1) x2 + 49 = 0 2) - 16x4 = 0 3) x8 - 16 = 0 4) 2x4 - 9x2 + 10 = 0 5) x5 + 2x4 - 3x3 - 6x2 + 2x + 4 = 0

Найдем неизвестные.

1) x^2 + 49 = 0;

x^2 = - 49;

Нет корней.

2) - 16 * x^4 = 0;

x^4 = 0;

x = 0.

3) x^8 - 16 = 0;

(x^4) ^2 - 4^2 = 0;

(x^4 - 4) * (x^4 + 4) = 0;

x^2 + 4 = 0 нет корней.

x^4 - 4 = 0;

(x^2 - 2) * (x^2 + 2) = 0;

x^2 - 2 = 0;

x^2 = 2;

x = √2;

x = - √2.

4) 2 * x^4 - 9 * x^2 + 10 = 0;

D = 81 - 4 * 2 * 10 = 1;

x^2 = (9 + 1) / (2 * 2) = 10/4 = 5/2 = 2.5;

x = √2.5;

x = - √2.58;

x^2 = (9 - 1) / 4 = 8/4 = 2;

x = √2;

x = - √2.

5) x^5 + 2 * x^4 - 3 * x^3 - 6 * x^2 + 2 * x + 4 = 0;

x^3 * (x^2 + 2 * x - 3) - 2 * (3 * x^2 + x + 2) = 0;

Нет корней.