вправа 725 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) x³ - 4x = 0;
x(x² - 4) = 0;
x(x - 2)(x + 2) = 0;
x = 0;
x - 2 = 0;
x = 2;
x + 2 = 0;
x = -2; \begin{equation}2)x^{4}-x^{2}=0;\end{equation} x²(x² - 1) = 0;
x²(x - 1)(x + 1) = 0;
x = 0;
x - 1 = 0;
x = 1;
x + 1 = 0;
x = -1; \begin{equation}3)x^{5}-36x^{3}=0;\end{equation} x³(x² - 36) = 0;
x³(x - 6)(x + 6) = 0;
x = 0;
x - 6 = 0;
x = 6;
x + 6 = 0;
x = -6;
4) 9x³ - x = 0;
x(9x² - 1) = 0;
x(3x - 1)(3x + 1) = 0;
x = 0;
3x - 1 = 0; \begin{equation}x=\frac{1}{3};\end{equation} 3x + 1 = 0; \begin{equation}x=-\frac{1}{3};\end{equation} 5) x³ - 10x² + 25x = 0;
x(x² - 10x + 25) = 0;
x(x - 5)² = 0;
x = 0;
x - 5 = 0;
x = 5;
6) x³ + 2x² - 9x - 18 = 0;
x²(x + 2) - 9(x + 2) = 0;
(x + 2)(x² - 9) = 0;
(x + 2)(x - 3)(x + 3) = 0;
x + 2 = 0;
x = -2;
x - 3 = 0;
x = 3;
x + 3 = 0;
x = -3;
7) x³ - 5x² + 4x - 20 = 0;
x²(x - 5) + 4(x - 5) = 0;
(x² + 4)(x - 5) = 0;
x² + 4 = 0;
коренів немає;
x - 5 = 0;
x = 5; \begin{equation}8)x^{5}-x^{4}-x+1=0;\end{equation} \begin{equation}x^{4}\left ( x-1 \right )-\left ( x-1 \right )=0;\end{equation} \begin{equation}\left ( x^{4}-1 \right )\left ( x-1 \right )=0;\end{equation} (x² - 1)(x² + 1)(x - 1) = 0;
(x - 1)(x + 1)(x² + 1)(x - 1) = 0;
(x - 1)²(x + 1)(x² + 1) = 0;
x - 1 = 0;
x = 1;
x + 1 = 0;
x = -1;
x² + 1 = 0;
коренів немає.