Разложение на множители
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/ _________________ \ / _________________ \ / _________________ \
| / ___ / ___\ | | / ___ / ___\ | | / ___ |
| 5 / 65 13*I*\/ 3 | 1 I*\/ 3 | 13 | | 5 / 65 13*I*\/ 3 | 1 I*\/ 3 | 13 | | 5 / 65 13*I*\/ 3 13 |
1*|c + - - 3 / -- + ---------- *|- - - -------| - ----------------------------------------|*|c + - - 3 / -- + ---------- *|- - + -------| - ----------------------------------------|*|c + - - 3 / -- + ---------- - ------------------------|
| 3 \/ 54 18 \ 2 2 / _________________| | 3 \/ 54 18 \ 2 2 / _________________| | 3 \/ 54 18 _________________|
| / ___\ / ___ | | / ___\ / ___ | | / ___ |
| | 1 I*\/ 3 | / 65 13*I*\/ 3 | | | 1 I*\/ 3 | / 65 13*I*\/ 3 | | / 65 13*I*\/ 3 |
| 9*|- - - -------|*3 / -- + ---------- | | 9*|- - + -------|*3 / -- + ---------- | | 9*3 / -- + ---------- |
\ \ 2 2 / \/ 54 18 / \ \ 2 2 / \/ 54 18 / \ \/ 54 18 /
$$1 \left(c - \left(- \frac{5}{3} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}} + \frac{13}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}}}\right)\right) \left(c - \left(- \frac{5}{3} + \frac{13}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}}\right)\right) \left(c - \left(- \frac{5}{3} + \frac{13}{9 \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}}} + \sqrt[3]{\frac{65}{54} + \frac{13 \sqrt{3} i}{18}}\right)\right)$$
((1*(c + (5/3 - (65/54 + 13*i*sqrt(3)/18)^(1/3)*(-1/2 - i*sqrt(3)/2) - 13/(9*(-1/2 - i*sqrt(3)/2)*(65/54 + 13*i*sqrt(3)/18)^(1/3)))))*(c + (5/3 - (65/54 + 13*i*sqrt(3)/18)^(1/3)*(-1/2 + i*sqrt(3)/2) - 13/(9*(-1/2 + i*sqrt(3)/2)*(65/54 + 13*i*sqrt(3)/18)^(1/3)))))*(c + (5/3 - (65/54 + 13*i*sqrt(3)/18)^(1/3) - 13/(9*(65/54 + 13*i*sqrt(3)/18)^(1/3))))
Подстановка условия
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c^3 + 5*c^2 + 4*c - 1*5 при c = 1
$$c^{3} + 5 c^{2} + 4 c - 5$$
$$c^{3} + 5 c^{2} + 4 c - 5$$
$$c = 1$$
3 2
-5 + (1) + 4*(1) + 5*(1)
$$(1)^{3} + 5 (1)^{2} + 4 (1) - 5$$
$$-5 + 1^{3} + 4 \cdot 1 + 5 \cdot 1^{2}$$
$$5$$