Господин Экзамен
(x+2)*(x+1)*(x-2)+(x-7/2)*((3+2*x)*(x-2)+(x+2)*(x+1)) если x=-3/2
Решение
Вы ввели
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(x + 2)*(x + 1)*(x - 2) + (x - 7/2)*((3 + 2*x)*(x - 2) + (x + 2)*(x + 1))
$$\left(x + 1\right) \left(x + 2\right) \left(x - 2\right) + \left(x - \frac{7}{2}\right) \left(\left(x + 1\right) \left(x + 2\right) + \left(x - 2\right) \left(2 x + 3\right)\right)$$
(x + 2)*(x + 1)*(x - 1*2) + (x - 1*7/2)*((3 + 2*x)*(x - 1*2) + (x + 2)*(x + 1))
Общее упрощение
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2
3 15*x
10 - 15*x + 4*x - -----
2
$$4 x^{3} - \frac{15 x^{2}}{2} - 15 x + 10$$
10 - 15*x + 4*x^3 - 15*x^2/2
Разложение на множители
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/ ___________________ \ / ___________________ \ / ___________________ \ | / _____ / ___\ | | / _____ / ___\ | | / _____ | | 5 / 85 5*I*\/ 719 | 1 I*\/ 3 | 105 | | 5 / 85 5*I*\/ 719 | 1 I*\/ 3 | 105 | | 5 / 85 5*I*\/ 719 105 | 1*|x + - - - 3 / --- + ----------- *|- - - -------| - -------------------------------------------|*|x + - - - 3 / --- + ----------- *|- - + -------| - -------------------------------------------|*|x + - - - 3 / --- + ----------- - ---------------------------| | 8 \/ 512 64 \ 2 2 / ___________________| | 8 \/ 512 64 \ 2 2 / ___________________| | 8 \/ 512 64 ___________________| | / ___\ / _____ | | / ___\ / _____ | | / _____ | | | 1 I*\/ 3 | / 85 5*I*\/ 719 | | | 1 I*\/ 3 | / 85 5*I*\/ 719 | | / 85 5*I*\/ 719 | | 64*|- - - -------|*3 / --- + ----------- | | 64*|- - + -------|*3 / --- + ----------- | | 64*3 / --- + ----------- | \ \ 2 2 / \/ 512 64 / \ \ 2 2 / \/ 512 64 / \ \/ 512 64 /
$$1 \left(x - \left(\frac{5}{8} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}} + \frac{105}{64 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}}}\right)\right) \left(x - \left(\frac{5}{8} + \frac{105}{64 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}}\right)\right) \left(x - \left(\frac{5}{8} + \frac{105}{64 \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}}} + \sqrt[3]{\frac{85}{512} + \frac{5 \sqrt{719} i}{64}}\right)\right)$$
((1*(x - (5/8 - (85/512 + 5*i*sqrt(719)/64)^(1/3)*(-1/2 - i*sqrt(3)/2) - 105/(64*(-1/2 - i*sqrt(3)/2)*(85/512 + 5*i*sqrt(719)/64)^(1/3)))))*(x - (5/8 - (85/512 + 5*i*sqrt(719)/64)^(1/3)*(-1/2 + i*sqrt(3)/2) - 105/(64*(-1/2 + i*sqrt(3)/2)*(85/512 + 5*i*sqrt(719)/64)^(1/3)))))*(x - (5/8 - (85/512 + 5*i*sqrt(719)/64)^(1/3) - 105/(64*(85/512 + 5*i*sqrt(719)/64)^(1/3))))
Подстановка условия
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(x + 2)*(x + 1)*(x - 1*2) + (x - 1*7/2)*((3 + 2*x)*(x - 1*2) + (x + 2)*(x + 1)) при x = -3/2
подставляем
(x + 2)*(x + 1)*(x - 2) + (x - 7/2)*((3 + 2*x)*(x - 2) + (x + 2)*(x + 1))
$$\left(x + 1\right) \left(x + 2\right) \left(x - 2\right) + \left(x - \frac{7}{2}\right) \left(\left(x + 1\right) \left(x + 2\right) + \left(x - 2\right) \left(2 x + 3\right)\right)$$
2
3 15*x
10 - 15*x + 4*x - -----
2
$$4 x^{3} - \frac{15 x^{2}}{2} - 15 x + 10$$
переменные
x = -3/2
$$x = - \frac{3}{2}$$
2
3 15*(-3/2)
10 - 15*(-3/2) + 4*(-3/2) - ----------
2
$$4 (-3/2)^{3} - \frac{15 (-3/2)^{2}}{2} - 15 (-3/2) + 10$$
17/8
$$\frac{17}{8}$$
17/8
Рациональный знаменатель
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2
3 15*x
10 - 15*x + 4*x - -----
2
$$4 x^{3} - \frac{15 x^{2}}{2} - 15 x + 10$$
(-7 + 2*x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + 2*(1 + x)*(-2 + x)*(2 + x)
------------------------------------------------------------------------------
2
$$\frac{2 \left(x - 2\right) \left(x + 1\right) \left(x + 2\right) + \left(2 x - 7\right) \left(\left(x - 2\right) \left(2 x + 3\right) + \left(x + 1\right) \left(x + 2\right)\right)}{2}$$
((-7 + 2*x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + 2*(1 + x)*(-2 + x)*(2 + x))/2
Собрать выражение
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(-7/2 + x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + (1 + x)*(-2 + x)*(2 + x)
$$\left(x - 2\right) \left(x + 1\right) \left(x + 2\right) + \left(x - \frac{7}{2}\right) \left(\left(x - 2\right) \left(2 x + 3\right) + \left(x + 1\right) \left(x + 2\right)\right)$$
(-7/2 + x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + (1 + x)*(-2 + x)*(2 + x)
Общий знаменатель
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2
3 15*x
10 - 15*x + 4*x - -----
2
$$4 x^{3} - \frac{15 x^{2}}{2} - 15 x + 10$$
10 - 15*x + 4*x^3 - 15*x^2/2
Комбинаторика
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2
3 15*x
10 - 15*x + 4*x - -----
2
$$4 x^{3} - \frac{15 x^{2}}{2} - 15 x + 10$$
10 - 15*x + 4*x^3 - 15*x^2/2
Степени
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(-7/2 + x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + (1 + x)*(-2 + x)*(2 + x)
$$\left(x - 2\right) \left(x + 1\right) \left(x + 2\right) + \left(x - \frac{7}{2}\right) \left(\left(x - 2\right) \left(2 x + 3\right) + \left(x + 1\right) \left(x + 2\right)\right)$$
(-7/2 + x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + (1 + x)*(-2 + x)*(2 + x)
Численный ответ
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(-3.5 + x)*((1.0 + x)*(2.0 + x) + (3.0 + 2.0*x)*(-2.0 + x)) + (1.0 + x)*(2.0 + x)*(-2.0 + x)
(-3.5 + x)*((1.0 + x)*(2.0 + x) + (3.0 + 2.0*x)*(-2.0 + x)) + (1.0 + x)*(2.0 + x)*(-2.0 + x)
Объединение рациональных выражений
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(-7 + 2*x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + 2*(1 + x)*(-2 + x)*(2 + x)
------------------------------------------------------------------------------
2
$$\frac{2 \left(x - 2\right) \left(x + 1\right) \left(x + 2\right) + \left(2 x - 7\right) \left(\left(x - 2\right) \left(2 x + 3\right) + \left(x + 1\right) \left(x + 2\right)\right)}{2}$$
((-7 + 2*x)*((1 + x)*(2 + x) + (-2 + x)*(3 + 2*x)) + 2*(1 + x)*(-2 + x)*(2 + x))/2