Mr and Mrs Davis have a son. His name is Bobby, and it was his birthday a few days ago.
Last Sunday Bobby's grandfather came to visit them, and he brought Bobby a nice toy train. When he gave it to Bobby, he said: "I'm sorry, Bobby, but I forgot your birthday last Tuesday, so I give you this present then."
"Oh, that doesn't matter Grandpa," Bobby answered. "Thank you very much. It's just what I wanted."
"And how old are you now, Bobby?" his grandfather asked. Bobby knew the answer to that question. "I'm five, Grandpa," he said.
"That's good," the old man said. "You're a big boy now, Bobby. And what are you going to be when you're older?" Bobby knew the answer to that question, too. "I' m going to be six, Grandpa," he answered Этот?
2*4^x-3*10^x=5*25^xРазделим правую и левую части на 25^x. Получим 4^x 10^x2 - 3 = 5 25^x 25^x Так как степени у числетелей и знаменателей одинаковые можно поступить следующим образом 2* (4 : 25)^х - 3*(10 : 25)^х = 5Во второй дроби можно сократить 10 и 25 на 5. Получаем 2* (4 : 25)^х - 3*(2 : 5)^х = 5 Так как 4 = 2^2, a 25 = 5^2, получим следующее 2* (2 : 5)^2х - 3*(2 : 5)^х = 5 Введем новую переменную t = (2 : 5)^хПолучим новое уравнение2*t^2 - 3*t = 52*t^2 - 3*t - 5 = 0Решаем через дискриминант. a = 2, b = -3, c = -5D = b^2 -4ac = 9 - 4*2*(-5) = 9 + 40 = 49t(1) = (3 - 7) : 4 = -1t(2) = (3 + 7) : 4 = 2,5 x = -1 нам не подходит, так как ни при каких х (2 : 5)^х не будет отрицательным.Тогда получаем (2 : 5)^х = t(2) (2 : 5)^х = 5 : 2 (2 : 5)^х = (2 : 5)^(-1) х = -1 ответ: х = -1
У меня получилось 4 таких числа - 1236, 1248, 1296 и 1326. Это навскидку, может и еще есть. Очевидно, первая цифра 1. Если все цифры различны, то вторая 2 или 3. Если вторая цифра 2, то третья не меньше 3, а последняя четная. Если третья 3, то число делится на 2 и 3, то есть на 6. Последняя 6. 1236 делится на 2,3 и 6. Если третья 4, то последняя 8. 1248 делится на 2, 4 и 8. Третья не может быть 5,6,7,и 8, по разным причинам. Если третья 9, то последняя 6, 1296 делится на 2, 9 и 6. Если вторая 3, то получается 1326 - четное и делится на 6.
Mr and Mrs Davis have a son. His name is Bobby, and it was his birthday a few days ago.
Last Sunday Bobby's grandfather came to visit them, and he brought Bobby a nice toy train. When he gave it to Bobby, he said: "I'm sorry, Bobby, but I forgot your birthday last Tuesday, so I give you this present then."
"Oh, that doesn't matter Grandpa," Bobby answered. "Thank you very much. It's just what I wanted."
"And how old are you now, Bobby?" his grandfather asked. Bobby knew the answer to that question. "I'm five, Grandpa," he said.
"That's good," the old man said. "You're a big boy now, Bobby. And what are you going to be when you're older?" Bobby knew the answer to that question, too. "I' m going to be six, Grandpa," he answered
Этот?