Предмет: Математика, автор: versachexdior

математика задача №3
Если x и y действительные числа, какое наименьшее значение может принимать выражение (2ху-1)²+(х+2у)² ?
A 0
B 0.25
C 0.5
D 1
E 2

CrossFord: Так как квадраты - числа неотрицательные, то наименьшее значение этого выражения достигается, когда оба подстепенных выражения равны 0.
Составим систему:
2xy-1=0
{
x+2y=0

Равносильная система:
2xy=1
{
x^2+2xy=0

Вычтем первое из второго:

Удачи извлекать корень из -1 (см. "Комплексные числа")

Ответы

Автор ответа: CrossFord

Раскроем скобки и преобразуем. Получим в итоге:

$4x^{2} y^{2} +x^{2} +4y^{2} +1$

Поймем, что все эти числа неотрицательные. Тогда наименьшее значение будет достигаться тогда, когда все одночлены с переменными равны 0. Ну и тогда наименьшее значение равняется константе 1.

Ответ: D

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Militia of the Republic of Belarus
(1) The first militia forces in Belarus were created in 1917. The Militia of the Republic of Belarus, which comes under the authority of the Ministry of Internal Affairs, has a wide range of activity. Its activity is regu-lated by the Law on Militia of the Republic of Belarus, adopted in 1991, and amended several twice.
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(4) Under the law, the central objective of the law enforcement agencies is to provide security or, at least, a social and psychological feeling of security, to a majority of citizens, in a majority of places for most of the time. Nowadays great attention in the work of militia is also paid to prevention of crime, to its suppression. But if a crime has been committed, the militia officers are to solve the crime as quickly as possible. To fulfill these tasks the law-enforcement agencies are composed of different departments.
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