thắc mắc nhỏ về bất phương trình

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dominhngoc95

[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
Chắc suất Đại học top - Giữ chỗ ngay!!

ĐĂNG BÀI NGAY để cùng trao đổi với các thành viên siêu nhiệt tình & dễ thương trên diễn đàn.

em thấy có nhiều bài khi đặt ẩn phụ t phải đặt điều kiện cho t nhưng cũng có 1 vài bài không cần đặt điều kiện cho t vậy khi nào cần đặt dk khi nào không ak. ai có thể giải thich giúp với
đây là 2 vidu cụ thể VD1giai pt : (x-3)(x+1) + 4(x-3)xcănbac2 của(x+1)/(x-3)=-3 bài nầy e thấy lời giải của thầy giáo ko cần đăt điều kiện cho t
VD2 giai pt x2-2căn(x2+13)=22 còn bai nay thi phải co điều kiên
 
T

truongduong9083

Bạn hiểu đơn giản là
1. $t = (x-1).\sqrt{\dfrac{x}{x-1}}$ thì chỉ có điều kiện cho ẩn x thôi nhé, còn t thì luôn xác định trên TXĐ của biến x rồi (Có thể trong trường hợp này để chặt chẽ ta chỉ cần lấy điều kiện $t \neq 0$)
2. $t = \sqrt{x^2-1}$ trong trường hợp này thì $t \geq 0$ bạn nhé
Với bài toán tìm m (Phương trình, bất phương trình có nghiệm ...) thì điều kiện rất quan trọng nên bạn chú ý cách đặt điều kiện nhé
 
Last edited by a moderator:
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nguyenbahiep1

trong 1 bài tập về giải phương trình thì khi đặt ẩn phụ ta có thể ko cần đặt điều kiện của ẩn phụ (t,u,v...) nhưng bước cuối thì phải có thêm 1 bước là thay lại nghiệm vào pt xem có thỏa mãn hay ko


Đương nhiên nên đặt dk cho ẩn phụ để bài toán được giải triệt để ngay từ đầu

CHú ý đối với bất phương trình thì bất buộc phải có điều kiện khi đặt ẩn phụ
 
D

dominhngoc95

trong 1 bài tập về giải phương trình thì khi đặt ẩn phụ ta có thể ko cần đặt điều kiện của ẩn phụ (t,u,v...) nhưng bước cuối thì phải có thêm 1 bước là thay lại nghiệm vào pt xem có thỏa mãn hay ko


Đương nhiên nên đặt dk cho ẩn phụ để bài toán được giải triệt để ngay từ đầu

CHú ý đối với bất phương trình thì bất buộc phải có điều kiện khi đặt ẩn phụ
sao mình thấy nhiều bài giải phương trình đơn giản thầy giáo vẫn đặt điêu kiện cho ẩn phụ bình thường mà tìm min max cho t
 
N

nguyenbahiep1

sao mình thấy nhiều bài giải phương trình đơn giản thầy giáo vẫn đặt điêu kiện cho ẩn phụ bình thường mà tìm min max cho t


thì đã bảo rồi đó

thứ nhất là giải được triệt để bài toán ko cần thử lại nghiệm

thứ 2 có thể ảnh hưởng đến câu thứ 2 ví dụ biện luận theo m để pt có .............

Ví dụ: giải pt

[TEX]2^{2x} + 3.m.2^x - 4 = 0 [/TEX]

câu a giải pt khi m = 1

câu b tìm m để pt có 2 nghiệm phân biệt

vậy ở câu 1 khi đặt ẩn phụ [TEX]t = 2^x[/TEX]

dù bạn ko có điều kiện t> 0

khi thay lại ta vẫn loại nghiệm [TEX]2^x = - 4 [/TEX]

nhưng ở câu hai thì lại phải bắt buộc phải đặt điều kiện cho t đế giải được tham số m
 
V

VefCreefcrync

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