Квадратные корни

Урок по теме «Квадратные корни» Алгебра, 8 класс

МОУ СОШ № 31,

г.Ростов-на-Дону,

учитель математики

Кряквина Л.Н.

2005 год

Содержание

• 1. Понятие квадратного корня из неотрицательного числа.
• 2. Функция y=√x , ее свойства и график.
• 3. Свойства квадратных корней.
• 4. Математический диктант.
• 5. Вопросы для самоконтроля.

Понятие квадратного корня из неотрицательного числа

• Квадратным корнем из неотрицательного числа a называют такое неотрицательное число, квадрат которого равен a . Это число обозначают √ a , число при этом называют подкоренным числом.

Определения

• Операцию нахождения квадратного корня из неотрицательного числа называют извлечением квадратного корня. Эта операция является обратной по отношению к возведению в квадрат. Например, 5 2 =25 и √25=5.

Используем следующую таблицу для построения графика функции

X 0

1

Y 0

1

4

6,25

2

2,5

9

16

3

4

Построим найденные точки (0;0), (1;1), (4;2), (6,25;2,5) , (9;3) , (16;4)

в координатной плоскости. Они располагаются на некоторой

линии, начертим ее. Получили график функции y= √x.

График функции квадратного корня

Λ

›

0 при х 0 . 3. Функция непрерывна на луче [ 0 ;+∞) . 4. Функция ограничена снизу и не ограничена сверху. 5. у наим =0 (достигается при х=0), у наиб не существует. " width="640"

Функция квадратного корня

• Свойства функции y= √ x :
• 1. Область определения функции – луч [ 0 ;+∞) .
• 2. у=0 при х=0 ; у 0 при х 0 .
• 3. Функция непрерывна на луче [ 0 ;+∞) .
• 4. Функция ограничена снизу и не ограничена сверху.
• 5. у наим =0 (достигается при х=0), у наиб не существует.

Свойства квадратных корней

Математический диктант

• Учитель предлагает учащимся плакат с утверждениями, некоторые из которых содержат ошибки или неточности. Учащиеся должны

• определить верные и неверные утверждения. Свой ответ они должны аргументировать, ссылаясь на известные свойства и правила.

Текст математического диктанта

?

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• Если m
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• m 4 = size 12{ sqrt {m rSup { size 8{4} } } ={}} {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAATMFAAA/ AgAALQAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAADIFAAA+AgAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAFwCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAA9wEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAABcAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABHAwAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAADcAQAAAQBtMQEA AAAAAQABAG0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24g U2VyaWYAAAAAAAAZAQAAAAADAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAsAIAACMBAAABADSNAAAAAAAB AAEANACMAAEAAAAAAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJvbAAAAAAA AKYBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEABQAA AP////8AhgABAAQAAAAAAAAAcgACABoAAABPAwAA3AEAAAEAAAA9AE8BAAAAAAEAAQA9AIwA AQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA m 2 .
• a a 2 size 12{ sqrt {a rSup { size 8{2} } } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAWYDAAA/ AgAAJgAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAGUDAAA+AgAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAFwCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAA9wEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAABcAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAADdAgAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAADcAQAAAQBh0wAA AAAAAQABAGEAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24g U2VyaWYAAAAAAAAZAQAAAAADAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAARgIAACMBAAABADKNAAAAAAAB AAEAMgCMAAEAAAAAAJUAAQAEAAAAAAAAAJYAAQACAAAACQCMAAEAAAAAAA== = a 2 .

Тест

Задание № 1

• Чему равен √3364?
• 1. 58
• 2. 52
• 3. 56
• 4. 62

Задание № 2

• Чему равно значение числового выражения ⅔ ٠ √ 150 ٠ 0,25 ٠ √ 6 ?

• 1. 5
• 2 30
• 3. 12
• 4. 6

Задание № 3

• Упростите выражение √75 b 7 : √3 b 3 .
• 1. 25b 4
• 2. 3b 4
• 3. -3b 4
• 4. 5b 2

Задание № 4

• Найдите наименьшее значение функции y= √x+1 на отрезке [-1,1].
• 1. 2
• 2. -2
• 3. 0
• 4. 1

Задания для самоконтроля

• Вычислите: а) 2 6 7 2 size 12{ sqrt {2 rSup { size 8{6} } 7 rSup { size 8{2} } } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAfUEAAA/ AgAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAPQEAAA+AgAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAFwCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAA9wEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAABcAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABsBAAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAADcAQAAAQAy0wAA AAAAAQABADIAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24g U2VyaWYAAAAAAAAZAQAAAAADAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAARgIAACMBAAABADaNAAAAAAAB AAEANgCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAD/AgAA3AEAAAEAN9MAAAAAAAEAAQA3 AIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNlcmlmAAAA AAAAGQEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAANMDAAAjAQAAAQAyjQAAAAAAAQABADIAjAAB AAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= , б) 13 4 9 . size 12{ sqrt {"13" { {4} over {9} } "." } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAaMFAAA9 BAAAPQAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAKIFAAA8BAAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAANYEAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAA7QMAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAADWBAAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAAAaBQAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAHIBAADKAgAAAgAxM6YB AAAAAAIAAgAxADMAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRp b24gU2VyaWYAAAAAAACmAQAAAAADAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEA AgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAaQMAANwBAAABADTTAAAA AAABAAEANACMAAEAAAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoA AQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAA AAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAA AE8DAABGAgAAaAQAAFoCAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGli ZXJhdGlvbiBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAA AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAABpAwAA7QMAAAEA OdMAAAAAAAEAAQA5AIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAKcEAADKAgAAAQAuagAA AAAAAQABAC4AjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA=
• Сравните: 5 3 size 12{ sqrt {3} } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAc8CAAD5 AQAAHwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAM4CAAD4AQAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAAUCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAwgEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAAAFAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABGAgAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAACnAQAAAQAz0wAA AAAAAQABADMAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= и 6 2 size 12{ sqrt {2} } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAcoCAAD5 AQAAHwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAMkCAAD4AQAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAAUCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAwgEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAAAFAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABBAgAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAACnAQAAAQAy0wAA AAAAAQABADIAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= .

а)75 x 3 y 6 , size 12{ sqrt {x rSup { size 8{3} } y rSup { size 8{6} } ,} } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAdMFAAA/ AgAAOwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAANIFAAA+AgAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAFwCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAA9wEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAABcAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABKBQAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAI0BAADcAQAAAQB4uwAA AAAAAQABAHgAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24g U2VyaWYAAAAAAAAZAQAAAAADAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAARgIAACMBAAABADONAAAAAAAB AAEAMwCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAABPAwAA3AEAAAEAebsAAAAAAAEAAQB5 AIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNlcmlmAAAA AAAAGQEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAACIEAAAjAQAAAQA2jQAAAAAAAQABADYAjAAB AAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAACm AQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/ ////AIYAAQAEAAAAAAAAAHIAAgAXAAAA3AQAANwBAAABACxqAAAAAAABAAEALACMAAEAAAAA AJUAAQAEAAAAAAAAAJYAAQACAAAACQCMAAEAAAAAAA== где y

Упростите выражение: 2 2 + 50 − 98 size 12{ sqrt {2} + sqrt {"50"} - sqrt {"98"} } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbEKAAD5 AQAAWwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALAKAAD4AQAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJv bAAApgEAAAUCAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAwgEAAAEAAAAaIuEAAAAAAAEA AQAaIowAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAKYBAAAFAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAWAEA ABoAAABBAgAAKAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHIBAACnAQAAAQAy0wAA AAAAAQABADIAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wA AAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAARgIAAKcBAAABAAAAKwD2AAAAAAABAAEA KwCMAAEAAAAAAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJvbAAApgEAAAUC AAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEABQAAAP// //8AhgABAAQAAAAAAAAAcgACABoAAABpAwAAwgEAAAEAAAAaIuEAAAAAAAEAAQAaIowAAQAA AAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYAAAAK AE9wZW5TeW1ib2wAAKYBAAAFAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACI AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAPQQAABoAAAD9BQAA KAAAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNlcmlm AAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAFcEAACnAQAAAgA1MKYBAAAAAAIAAgA1 ADAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACm AQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/ ////AIYAAQAEAAAAAAAAAHIAAgAaAAAAGQYAAKcBAAABAAAAEiJPAQAAAAABAAEAEiKMAAEA AAAAAIsAAQACAAAAHwCKAAEAPAAAAAMANgAAAAoAT3BlblN5bWJvbAAApgEAAAUCAAD//wAA AAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgAB AAQAAAAAAAAAcgACABoAAABxBwAAwgEAAAEAAAAaIuEAAAAAAAEAAQAaIowAAQAAAAAAiwAB AAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAKYBAAAFAgAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAXwgAABoAAAAmCgAAKAAAAIwA AQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAA pgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAFAAAA /////wCGAAEABAAAAAAAAAByAAIAGgAAAHoIAACnAQAAAgA5OKYBAAAAAAIAAgA5ADgAjAAB AAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= .

К сожалению, Вы ошиблись!