Произведение корней 5^x-6*x-3=0
Решение
Сумма и произведение корней
[src]
сумма
/ ___ \ / ___ \
|-\/ 5 *log(5) | |-\/ 5 *log(5) |
W|--------------| W|--------------, -1|
1 \ 30 / 1 \ 30 /
- - - ----------------- + - - - ---------------------
2 log(5) 2 log(5)
$$\left(- \frac{1}{2} - \frac{W\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}}\right) + \left(- \frac{1}{2} - \frac{W_{-1}\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}}\right)$$
=
/ ___ \ / ___ \
|-\/ 5 *log(5) | |-\/ 5 *log(5) |
W|--------------| W|--------------, -1|
\ 30 / \ 30 /
-1 - ----------------- - ---------------------
log(5) log(5)
$$-1 - \frac{W\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}} - \frac{W_{-1}\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}}$$
произведение
/ / ___ \\ / / ___ \\ | |-\/ 5 *log(5) || | |-\/ 5 *log(5) || | W|--------------|| | W|--------------, -1|| | 1 \ 30 /| | 1 \ 30 /| |- - - -----------------|*|- - - ---------------------| \ 2 log(5) / \ 2 log(5) /
$$\left(- \frac{1}{2} - \frac{W\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}}\right) \left(- \frac{1}{2} - \frac{W_{-1}\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right)}{\log{\left(5 \right)}}\right)$$
=
/ / ___ \ \ / / ___ \ \
| |-\/ 5 *log(5) | | | |-\/ 5 *log(5) | |
|2*W|--------------| + log(5)|*|2*W|--------------, -1| + log(5)|
\ \ 30 / / \ \ 30 / /
-----------------------------------------------------------------
2
4*log (5)
$$\frac{\left(2 W\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right) + \log{\left(5 \right)}\right) \left(2 W_{-1}\left(- \frac{\sqrt{5} \log{\left(5 \right)}}{30}\right) + \log{\left(5 \right)}\right)}{4 \log{\left(5 \right)}^{2}}$$