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Консультация № 180280
10.10.2010, 22:51
40.55 руб.
15.10.2010, 16:57
0
3
2
Здравствуйте,уважаемые эксперты!Помогите,пожалуйста,решить последнее неравенство
Огромное Вам спасибо.
Огромное Вам спасибо.
Обсуждение
Неизвестный
10.10.2010, 23:14
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович.
V(x^2-5x-36)+V(5x+x^2-36)<=2V(x^2-36).
x^2-5x-36+5x+x^2-36 +2√((x^2-36)^2-25x^2)<= 4x^2-144
2√((x^2-36)^2-25x^2)<=2x^2 - 72
√((x^2-36)^2-25x^2)<=x^2 - 36
(x^2-36)^2-25x^2<=(x^2 - 36)^2
25x^2>=0
х - любое, найдем ОДЗ:
1) x^2-5x-36>=0
x<=-4; x>=9
2) x^2+5x-36>=0
x<=-9; x>=4
3) x^2 -36>=0
x<=-6; x>=6
Итак, x<=-9; x>=9
Ответ:x<=-9; x>=9
V(x^2-5x-36)+V(5x+x^2-36)<=2V(x^2-36).
x^2-5x-36+5x+x^2-36 +2√((x^2-36)^2-25x^2)<= 4x^2-144
2√((x^2-36)^2-25x^2)<=2x^2 - 72
√((x^2-36)^2-25x^2)<=x^2 - 36
(x^2-36)^2-25x^2<=(x^2 - 36)^2
25x^2>=0
х - любое, найдем ОДЗ:
1) x^2-5x-36>=0
x<=-4; x>=9
2) x^2+5x-36>=0
x<=-9; x>=4
3) x^2 -36>=0
x<=-6; x>=6
Итак, x<=-9; x>=9
Ответ:x<=-9; x>=9
5
10.10.2010, 23:15
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович.
Область определения
1) x2-5x-36[$8805$]0
(x-9)(x+4)[$8805$]0
x[$8712$](-[$8734$];-4][$8746$][9;[$8734$])
2) x2+5x-36[$8805$]0
(x+9)(x-4)[$8805$]0
x[$8712$](-[$8734$];-9][$8746$][4;[$8734$])
3)x2-36[$8805$]0
x[$8712$](-[$8734$];-6][$8746$][6;[$8734$])
Пересечением этих трёх областей является областью определения x[$8712$](-[$8734$];-9][$8746$][9;[$8734$])
Так как корни неотрицательны, имеем право возвести в квадрат
x2-5x-36+x2+5x-36+2[$8730$]((x2-36)2-25x2)[$8804$]4(x2-36)
проведём замену x2-36=t (выражение заведомо неотрицательно, т.к. использовалось при определении ОДЗ)
2t+2[$8730$](t2-25x2)[$8804$]4t
[$8730$](t2-25x2)[$8804$]t
t2-25x2[$8804$]t2
25x2[$8805$]0
x2[$8805$]0
Следовательно, неравенство удовлетворяют все х, принадлежащие области определения.
x[$8712$](-[$8734$];-9][$8746$][9;[$8734$])
Область определения
1) x2-5x-36[$8805$]0
(x-9)(x+4)[$8805$]0
x[$8712$](-[$8734$];-4][$8746$][9;[$8734$])
2) x2+5x-36[$8805$]0
(x+9)(x-4)[$8805$]0
x[$8712$](-[$8734$];-9][$8746$][4;[$8734$])
3)x2-36[$8805$]0
x[$8712$](-[$8734$];-6][$8746$][6;[$8734$])
Пересечением этих трёх областей является областью определения x[$8712$](-[$8734$];-9][$8746$][9;[$8734$])
Так как корни неотрицательны, имеем право возвести в квадрат
x2-5x-36+x2+5x-36+2[$8730$]((x2-36)2-25x2)[$8804$]4(x2-36)
проведём замену x2-36=t (выражение заведомо неотрицательно, т.к. использовалось при определении ОДЗ)
2t+2[$8730$](t2-25x2)[$8804$]4t
[$8730$](t2-25x2)[$8804$]t
t2-25x2[$8804$]t2
25x2[$8805$]0
x2[$8805$]0
Следовательно, неравенство удовлетворяют все х, принадлежащие области определения.
x[$8712$](-[$8734$];-9][$8746$][9;[$8734$])
5
и.т.д.
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