Господин Экзамен
a^3-4*a^2+20*a-16 если a=4
Решение
Разложение на множители
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/ ________________ / ___\ \ / ________________ / ___\ \ | 3 / _____ | 1 I*\/ 3 | | | 3 / _____ | 1 I*\/ 3 | | / ________________ \ | 2*\/ 10 + 3*\/ 159 *|- - - -------| | | 2*\/ 10 + 3*\/ 159 *|- - + -------| | | 3 / _____ | | 4 \ 2 2 / 22 | | 4 \ 2 2 / 22 | | 4 2*\/ 10 + 3*\/ 159 22 | 1*|a + - - + ------------------------------------- - -------------------------------------|*|a + - - + ------------------------------------- - -------------------------------------|*|a + - - + --------------------- - ---------------------| | 3 3 ________________ / ___\| | 3 3 ________________ / ___\| | 3 3 ________________| | 3 / _____ | 1 I*\/ 3 || | 3 / _____ | 1 I*\/ 3 || | 3 / _____ | | 3*\/ 10 + 3*\/ 159 *|- - - -------|| | 3*\/ 10 + 3*\/ 159 *|- - + -------|| \ 3*\/ 10 + 3*\/ 159 / \ \ 2 2 // \ \ 2 2 //
$$1 \left(a - \left(\frac{4}{3} + \frac{22}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{10 + 3 \sqrt{159}}} - \frac{2 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{10 + 3 \sqrt{159}}}{3}\right)\right) \left(a - \left(\frac{4}{3} - \frac{2 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{10 + 3 \sqrt{159}}}{3} + \frac{22}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{10 + 3 \sqrt{159}}}\right)\right) \left(a - \left(- \frac{2 \sqrt[3]{10 + 3 \sqrt{159}}}{3} + \frac{4}{3} + \frac{22}{3 \sqrt[3]{10 + 3 \sqrt{159}}}\right)\right)$$
((1*(a - (4/3 + 2*(10 + 3*sqrt(159))^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 22/(3*(10 + 3*sqrt(159))^(1/3)*(-1/2 - i*sqrt(3)/2)))))*(a - (4/3 + 2*(10 + 3*sqrt(159))^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 22/(3*(10 + 3*sqrt(159))^(1/3)*(-1/2 + i*sqrt(3)/2)))))*(a - (4/3 + 2*(10 + 3*sqrt(159))^(1/3)/3 - 22/(3*(10 + 3*sqrt(159))^(1/3))))
Подстановка условия
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a^3 - 4*a^2 + 20*a - 1*16 при a = 4
подставляем
3 2 a - 4*a + 20*a - 16
$$a^{3} - 4 a^{2} + 20 a - 16$$
3 2 -16 + a - 4*a + 20*a
$$a^{3} - 4 a^{2} + 20 a - 16$$
переменные
a = 4
$$a = 4$$
3 2 -16 + (4) - 4*(4) + 20*(4)
$$(4)^{3} - 4 (4)^{2} + 20 (4) - 16$$
3 2 -16 + 4 - 4*4 + 20*4
$$- 4 \cdot 4^{2} - 16 + 4^{3} + 20 \cdot 4$$
64
$$64$$
64