Разложение на множители
[src]
/ / ___ ___\\ / / ___ ___\\ / / ___ ___\\ / / ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\ / / ___ ___ ___ ___\\
| | \/ 2 I*\/ 2 || | | \/ 2 I*\/ 2 || | |\/ 2 I*\/ 2 || | |\/ 2 I*\/ 2 || | | \/ 2 \/ 6 I*\/ 2 I*\/ 6 || | | \/ 2 \/ 6 I*\/ 2 I*\/ 6 || | |\/ 2 \/ 6 I*\/ 2 I*\/ 6 || | |\/ 2 \/ 6 I*\/ 6 I*\/ 2 || | | \/ 2 \/ 6 I*\/ 2 I*\/ 6 || | | \/ 2 \/ 6 I*\/ 6 I*\/ 2 || | | \/ 6 \/ 2 I*\/ 2 I*\/ 6 || | | \/ 6 \/ 2 I*\/ 2 I*\/ 6 ||
1*(m + 0)*|m - n*|- ----- - -------||*|m - n*|- ----- + -------||*|m - n*|----- - -------||*|m - n*|----- + -------||*|m - n*|- ----- + ----- + ------- + -------||*|m - n*|- ----- + ----- - ------- - -------||*|m - n*|----- + ----- - ------- + -------||*|m - n*|----- + ----- - ------- + -------||*|m - n*|- ----- - ----- - ------- + -------||*|m - n*|- ----- - ----- - ------- + -------||*|m - n*|- ----- + ----- + ------- + -------||*|m - n*|- ----- + ----- - ------- - -------||*(n + 0)
\ \ 2 2 // \ \ 2 2 // \ \ 2 2 // \ \ 2 2 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 // \ \ 4 4 4 4 //
$$1 \left(m + 0\right) \left(m - n \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(m - n \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(m - n \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(m - n \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(m - n \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4} + \frac{\sqrt{2} i}{4} + \frac{\sqrt{6} i}{4}\right)\right) \left(m - n \left(- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4} - \frac{\sqrt{6} i}{4} - \frac{\sqrt{2} i}{4}\right)\right) \left(m - n \left(\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4} - \frac{\sqrt{2} i}{4} + \frac{\sqrt{6} i}{4}\right)\right) \left(m - n \left(\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4} - \frac{\sqrt{6} i}{4} + \frac{\sqrt{2} i}{4}\right)\right) \left(m - n \left(- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} - \frac{\sqrt{2} i}{4} + \frac{\sqrt{6} i}{4}\right)\right) \left(m - n \left(- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} - \frac{\sqrt{6} i}{4} + \frac{\sqrt{2} i}{4}\right)\right) \left(m - n \left(- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4} + \frac{\sqrt{2} i}{4} + \frac{\sqrt{6} i}{4}\right)\right) \left(m - n \left(- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4} - \frac{\sqrt{6} i}{4} - \frac{\sqrt{2} i}{4}\right)\right) \left(n + 0\right)$$
(((((((((((((1*(m + 0))*(m - n*(-sqrt(2)/2 - i*sqrt(2)/2)))*(m - n*(-sqrt(2)/2 + i*sqrt(2)/2)))*(m - n*(sqrt(2)/2 - i*sqrt(2)/2)))*(m - n*(sqrt(2)/2 + i*sqrt(2)/2)))*(m - n*(-sqrt(2)/4 + sqrt(6)/4 + i*sqrt(2)/4 + i*sqrt(6)/4)))*(m - n*(-sqrt(2)/4 + sqrt(6)/4 - i*sqrt(2)/4 - i*sqrt(6)/4)))*(m - n*(sqrt(2)/4 + sqrt(6)/4 - i*sqrt(2)/4 + i*sqrt(6)/4)))*(m - n*(sqrt(2)/4 + sqrt(6)/4 - i*sqrt(6)/4 + i*sqrt(2)/4)))*(m - n*(-sqrt(2)/4 - sqrt(6)/4 - i*sqrt(2)/4 + i*sqrt(6)/4)))*(m - n*(-sqrt(2)/4 - sqrt(6)/4 - i*sqrt(6)/4 + i*sqrt(2)/4)))*(m - n*(-sqrt(6)/4 + sqrt(2)/4 + i*sqrt(2)/4 + i*sqrt(6)/4)))*(m - n*(-sqrt(6)/4 + sqrt(2)/4 - i*sqrt(2)/4 - i*sqrt(6)/4)))*(n + 0)
Подстановка условия
[src]
m^13*n + m*n^13 при m = -1/4
$$m^{13} n + m n^{13}$$
$$m n \left(m^{12} + n^{12}\right)$$
$$m = - \frac{1}{4}$$
/ 12 12\
(-1/4)*n*\(-1/4) + n /
$$(-1/4) n \left((-1/4)^{12} + n^{12}\right)$$
/ 12 12\
-n*\-1/4 + n /
------------------
4
$$- \frac{n \left(n^{12} + \left(- \frac{1}{4}\right)^{12}\right)}{4}$$
/ 1 12\
-n*|-------- + n |
\16777216 /
--------------------
4
$$- \frac{n \left(n^{12} + \frac{1}{16777216}\right)}{4}$$