вправа 726 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) x³ - x = 0;
x(x² - 1) = 0;
x(x - 1)(x + 1) = 0;
x = 0;
x - 1 = 0;
x = 1;
x + 1 = 0;
x = -1; \begin{equation}2)x^{4}+x^{2}=0;\end{equation} x²(x² + 1) = 0;
x² = 0;
x = 0;
x² + 1 = 0;
коренів немає; \begin{equation}3)x^{4}-8x^{3}=0;\end{equation} x³(x - 8) = 0;
x³ = 0;
x = 0;
x - 8 = 0;
x = 8;
4) 49x³ + 14x² + x = 0;
x(49x² + 14x + 1) = 0;
x(7x + 1)² = 0;
x = 0;
7x + 1 = 0; \begin{equation}x=-\frac{1}{7};\end{equation} 5) x³ + x² - x - 1 = 0;
x²(x + 1) - (x + 1) = 0;
(x + 1)(x² - 1) = 0;
(x + 1)(x - 1)(x + 1) = 0;
(x + 1)²(x - 1) = 0;
x + 1 = 0;
x = -1;
x - 1 = 0;
x = 1;
6) x³ - 4x² - 25x + 100 = 0;
x²(x - 4) - 25(x - 4) = 0;
(x² - 25)(x - 4) = 0;
(x - 5)(x + 5)(x - 4) = 0;
x - 5 = 0;
x = 5;
x + 5 = 0;
x = -5;
x - 4 = 0;
x = 4.