(город на английском) (страна на английском) (день/месяц/год - сегодня) Dear Ben, Thank you for your kind letter. It was interesting to know about your achievements in learning Japanese. In my letter I'm going to answer your questions. First of all, I learn English, Russian and German in my school. And I also learn Spanish on my own. Some students in my school learn French, but i choosed German, It's optional. Second, I would like to learn Chinese, because it's very popular language and there are so many Chinese people, and that's awesome. Chinese is very complicated, but interesting too. It sounds so sweet and beautiful. Finally, I think you are excellent that chosen such a language like Japanese. It is the official language of Japan - the great country with a great culture. That's off for now. I have to go. Take care, (имя)
(страна на английском)
(день/месяц/год - сегодня)
Dear Ben,
Thank you for your kind letter. It was interesting to know about your achievements in learning Japanese. In my letter I'm going to answer your questions.
First of all, I learn English, Russian and German in my school. And I also learn Spanish on my own. Some students in my school learn French, but i choosed German, It's optional.
Second, I would like to learn Chinese, because it's very popular language and there are so many Chinese people, and that's awesome. Chinese is very complicated, but interesting too. It sounds so sweet and beautiful.
Finally, I think you are excellent that chosen such a language like Japanese. It is the official language of Japan - the great country with a great culture.
That's off for now. I have to go.
Take care,
(имя)
{ a + b = 1
{ a^5 + b^5 = (1/2 - sin x) + (1/2 + sin x) = 1
Раскладываем a^5 + b^5 на множители
a^5 + b^5 = (a+b)(a^4 - a^3*b + a^2*b^2 - a*b^3 + b^4)
Подставляем данные из системы
1 = 1(a^4 - a^3*b + a^2*b^2 - a*b^3 + b^4)
Записываем в более привычном виде
(a^4 + b^4 + a^2*b^2 ) - (a^3*b + a*b^3) = 1
Выделяем полные квадраты
(a^4 + 2a^2*b^2 + b^4 - a^2*b^2) - ab*(a^2 + b^2) = 1
Сворачиваем в квадраты
(a^2 + b^2)^2 - a^2*b^2 - ab*(a^2 + b^2) = 1
Опять выделяем полные квадраты
(a^2 + 2ab + b^2 - 2ab)^2 - ab*(a^2 + 2ab + b^2 - 2ab) - a^2*b^2 = 1
Опять сворачиваем в квадраты
( (a+b)^2 - 2ab)^2 - ab( (a+b)^2 - 2ab) - a^2*b^2 = 1
Подставляем a+b = 1, отсюда (a+b)^2 = 1
(1 - 2ab)^2 - ab(1 - 2ab) - a^2*b^2 = 1
Раскрываем скобки
1 - 4ab + 4a^2*b^2 - ab + 2a^2*b^2 - a^2*b^2 = 1
Приводим подобные
-5ab + 5a^2*b^2 = 0
5ab(ab - 1) = 0
Решения:
1)
1/2 - sin x = 0
sin x = 1/2
x1 = pi/6 + 2pi*k; x2 = 5pi/6 + 2pi*k
2)
sin x = -1/2
x3 = -pi/6 + 2pi*k; x4 = -5pi/6 + 2pi*k
3)
1/4 - sin^2 x = 1
sin^2 x = 1/4 - 1 = -3/4 < 0
Корней нет.
ответ: x1 = pi/6 + 2pi*k; x2 = 5pi/6 + 2pi*k
x3 = -pi/6 + 2pi*k; x4 = -5pi/6 + 2pi*k