Решите уравнение:
а) $x^3 - 2x^2 - x + 2 = 0$;
б) $y^3 - y^2 = 16y - 16$;
в) $2y^3 - y^2 - 32y + 16 = 0$;
г) $4x^3 - 3x^2 = 4x - 3$.
$x^3 - 2x^2 - x + 2 = 0$
$(x^3 - 2x^2) - (x - 2) = 0$
$x^2(x - 2) - (x - 2) = 0$
$(x - 2)(x^2 - 1) = 0$
(x − 2)(x − 1)(x + 1) = 0
x − 2 = 0
$x_1 = 2$
x − 1 = 0
$x_2 = 1$
x + 1 = 0
$x_3 = -1$
Ответ:
$x_1 = 2$;
$x_2 = 1$;
$x_3 = -1$.
$y^3 - y^2 = 16y - 16$
$y^3 - y^2 - 16y + 16 = 0$
$(y^3 - y^2) - (16y + 16) = 0$
$y^2(y - 1) - 16(y - 1) = 0$
$(y - 1)(y^2 - 16) = 0$
(y − 1)(y − 4)(y + 4) = 0
y − 1 = 0
$y_1 = 1$
y − 4 = 0
$y_2 = 4$
y + 4 = 0
$y_3 = -4$
Ответ:
$y_1 = 1$;
$y_2 = 4$;
$y_3 = -4$.
$2y^3 - y^2 - 32y + 16 = 0$
$(2y^3 - y^2) - (32y - 16) = 0$
$y^2(2y - 1) - 16(2y - 1) = 0$
$(2y - 1)(y^2 - 16) = 0$
(2y − 1)(y − 4)(y + 4) = 0
2y − 1 = 0
2y = 1
$y_1 = 0,5$
y − 4 = 0
$y_2 = 4$
y + 4 = 0
$y_3 = -4$
Ответ:
$y_1 = 0,5$;
$y_2 = 4$;
$y_3 = -4$.
$4x^3 - 3x^2 = 4x - 3$
$4x^3 - 3x^2 - 4x + 3 = 0$
$(4x^3 - 3x^2) - (4x - 3) = 0$
$x^2(4x - 3) - (4x - 3) = 0$
$(4x - 3)(x^2 - 1) = 0$
$(4x - 3)(x - 1)(x + 1) = 0$
4x − 3 = 0
4x = 3
$x_1 = 0,75$
x − 1 = 0
$x_2 = 1$
x + 1 = 0
$x_3 = -1$
Ответ:
$x_1 = 0,75$;
$x_2 = 1$;
$x_3 = -1$.
Пожауйста, оцените решение
