Разложение на множители
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/ _____________ \ / _____________ \ / _____________ \ / _____________ \
| / ___ ___| | / ___ ___| | / ___ ___| | / ___ ___|
| 5 / 7 I*\/ 3 I*\/ 3 | | 5 / 7 I*\/ 3 I*\/ 3 | | 5 / 7 I*\/ 3 I*\/ 3 | | 5 / 7 I*\/ 3 I*\/ 3 |
1*|n + - + / - + ------- + -------|*|n + - - / - + ------- + -------|*|n + - + / - - ------- - -------|*|n + - - / - - ------- - -------|
\ 4 \/ 8 8 4 / \ 4 \/ 8 8 4 / \ 4 \/ 8 8 4 / \ 4 \/ 8 8 4 /
$$\left(n + \left(\frac{5}{4} - \sqrt{\frac{7}{8} + \frac{\sqrt{3} i}{8}} + \frac{\sqrt{3} i}{4}\right)\right) 1 \left(n + \left(\frac{5}{4} + \sqrt{\frac{7}{8} + \frac{\sqrt{3} i}{8}} + \frac{\sqrt{3} i}{4}\right)\right) \left(n + \left(\frac{5}{4} - \frac{\sqrt{3} i}{4} + \sqrt{\frac{7}{8} - \frac{\sqrt{3} i}{8}}\right)\right) \left(n - \left(- \frac{5}{4} + \sqrt{\frac{7}{8} - \frac{\sqrt{3} i}{8}} + \frac{\sqrt{3} i}{4}\right)\right)$$
(((1*(n + (5/4 + sqrt(7/8 + i*sqrt(3)/8) + i*sqrt(3)/4)))*(n + (5/4 - sqrt(7/8 + i*sqrt(3)/8) + i*sqrt(3)/4)))*(n + (5/4 + sqrt(7/8 - i*sqrt(3)/8) - i*sqrt(3)/4)))*(n + (5/4 - sqrt(7/8 - i*sqrt(3)/8) - i*sqrt(3)/4))
Подстановка условия
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n^4 + 5*n^3 + 8*n^2 + 4*n + 1 при n = 3/2
4 3 2
n + 5*n + 8*n + 4*n + 1
$$n^{4} + 5 n^{3} + 8 n^{2} + 4 n + 1$$
4 3 2
1 + n + 4*n + 5*n + 8*n
$$n^{4} + 5 n^{3} + 8 n^{2} + 4 n + 1$$
$$n = \frac{3}{2}$$
4 3 2
1 + (3/2) + 4*(3/2) + 5*(3/2) + 8*(3/2)
$$(3/2)^{4} + 5 (3/2)^{3} + 8 (3/2)^{2} + 4 (3/2) + 1$$
$$\frac{751}{16}$$