Дано

$$64^{2 x} + 64^{2 y} = 12$$

x + y ___
64 = 4*/ 2

$$64^{x + y} = 4 sqrt{2}$$
Ответ
$$x_{1} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{1} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$x_{2} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{2} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (-1 – sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (-1 – sqrt{3} i right )}right)$$
=

0.25 – 3.0215734278848*i

$$x_{3} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{3} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (-1 + sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (-1 + sqrt{3} i right )}right)$$
=

0.25 + 3.0215734278848*i

$$x_{4} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{4} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (1 – sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (1 – sqrt{3} i right )}right)$$
=

0.25 – 1.5107867139424*i

$$x_{5} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{5} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (1 + sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (1 + sqrt{3} i right )}right)$$
=

0.25 + 1.5107867139424*i

$$x_{6} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$y_{6} = frac{1}{4} + frac{i pi}{log{left (2 right )}}$$
=
$$frac{1}{4} + frac{i pi}{log{left (2 right )}}$$
=

0.25 + 4.53236014182719*i

$$x_{7} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{7} = frac{1}{6}$$
=
$$frac{1}{6}$$
=

0.166666666666667

$$x_{8} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{8} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (-1 – sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (-1 – sqrt{3} i right )}right)$$
=

0.166666666666667 – 3.0215734278848*i

$$x_{9} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{9} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (-1 + sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (-1 + sqrt{3} i right )}right)$$
=

0.166666666666667 + 3.0215734278848*i

$$x_{10} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{10} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (1 – sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (1 – sqrt{3} i right )}right)$$
=

0.166666666666667 – 1.5107867139424*i

$$x_{11} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{11} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (1 + sqrt{3} i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (1 + sqrt{3} i right )}right)$$
=

0.166666666666667 + 1.5107867139424*i

$$x_{12} = frac{1}{4}$$
=
$$frac{1}{4}$$
=

0.25

$$y_{12} = frac{1}{6} + frac{i pi}{log{left (2 right )}}$$
=
$$frac{1}{6} + frac{i pi}{log{left (2 right )}}$$
=

0.166666666666667 + 4.53236014182719*i

$$x_{13} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{13} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (- sqrt{3} – i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (- sqrt{3} – i right )}right)$$
=

0.25 – 3.77696678485599*i

$$x_{14} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{14} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (- sqrt{3} + i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (- sqrt{3} + i right )}right)$$
=

0.25 + 3.77696678485599*i

$$x_{15} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{15} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (sqrt{3} – i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (sqrt{3} – i right )}right)$$
=

0.25 – 0.755393356971199*i

$$x_{16} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{16} = frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (sqrt{3} + i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{4} log{left (8 right )} + log{left (sqrt{3} + i right )}right)$$
=

0.25 + 0.755393356971199*i

$$x_{17} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{17} = frac{log{left (sqrt[4]{2} i right )}}{log{left (2 right )}}$$
=
$$frac{log{left (sqrt[4]{2} i right )}}{log{left (2 right )}}$$
=

0.25 + 2.2661800709136*i

$$x_{18} = frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=
$$frac{log{left (2 right )} + i pi}{6 log{left (2 right )}}$$
=

0.166666666666667 + 0.755393356971199*i

$$y_{18} = frac{1}{4} – frac{i pi}{2 log{left (2 right )}}$$
=
$$frac{1}{4} – frac{i pi}{2 log{left (2 right )}}$$
=

0.25 – 2.2661800709136*i

$$x_{19} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{19} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (- sqrt{3} – i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (- sqrt{3} – i right )}right)$$
=

0.166666666666667 – 3.77696678485599*i

$$x_{20} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{20} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (- sqrt{3} + i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (- sqrt{3} + i right )}right)$$
=

0.166666666666667 + 3.77696678485599*i

$$x_{21} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{21} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (sqrt{3} – i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (sqrt{3} – i right )}right)$$
=

0.166666666666667 – 0.755393356971199*i

$$x_{22} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{22} = frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (sqrt{3} + i right )}right)$$
=
$$frac{1}{log{left (2 right )}} left(- frac{1}{6} log{left (32 right )} + log{left (sqrt{3} + i right )}right)$$
=

0.166666666666667 + 0.755393356971199*i

$$x_{23} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{23} = frac{log{left (sqrt[6]{2} i right )}}{log{left (2 right )}}$$
=
$$frac{log{left (sqrt[6]{2} i right )}}{log{left (2 right )}}$$
=

0.166666666666667 + 2.2661800709136*i

$$x_{24} = frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + 2 i pi}{12 log{left (2 right )}}$$
=

0.25 + 0.755393356971199*i

$$y_{24} = frac{1}{6} – frac{i pi}{2 log{left (2 right )}}$$
=
$$frac{1}{6} – frac{i pi}{2 log{left (2 right )}}$$
=

0.166666666666667 – 2.2661800709136*i

Численный ответ

x1 = 0.250000000000000
y1 = 0.1666666666666667

   
4.81
Pomogashka
13 лет занимаюсь написанием курсовых, контрольных, дипломных работ, рефератов, отчетов по практике. Всегда доводила студентов до защиты. Оценки только положительные. Каждая работа уникальна и грамотно написана.Очень люблю свою работу.