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Giải mục 2 trang 12, 13 SGK Toán 9 tập 2 - Kết nối tri thức

Giải các phương trình sau: a) (2{x^2} + 6x = 0); b) (5{x^2} + 11x = 0).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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LT2

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 2 trang 12 SGK Toán 9 Kết nối tri thức

Giải các phương trình sau: a) \(2{x^2} + 6x = 0\); b) \(5{x^2} + 11x = 0\).

Phương pháp giải:

Các bước giải phương trình: + Bước 1: Đưa phương trình về dạng: \(A.B = 0\). + Bước 2: Nếu \(A.B = 0\) thì \(A = 0\) hoặc \(B = 0\). Giải các phương trình đó và kết luận.

Lời giải chi tiết:

a) \(2{x^2} + 6x = 0\) \(2x\left( {x + 3} \right) = 0\) \(x = 0\) hoặc \(x =  - 3\) Vậy phương trình có hai nghiệm \(x = 0\); \(x =  - 3\). b) \(5{x^2} + 11x = 0\) \(x\left( {5x + 11} \right) = 0\) \(x = 0\) hoặc \(x =  - \frac{{11}}{5}\) Vậy phương trình có hai nghiệm \(x = 0\); \(x =  - \frac{{11}}{5}\).

LT3

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 3 trang 12 SGK Toán 9 Kết nối tri thức

Giải các phương trình sau: a) \({x^2} - 25 = 0\); b) \({\left( {x + 3} \right)^2} = 5\).

Phương pháp giải:

Các bước giải phương trình: + Bước 1: Đưa phương trình về dạng: \({A^2} = B\left( {B \ge 0} \right)\). + Bước 2: Nếu \({A^2} = B\left( {B \ge 0} \right)\) thì \(A = \sqrt B \) hoặc \(A =  - \sqrt B \). Giải các phương trình đó và kết luận.

Lời giải chi tiết:

a) \({x^2} - 25 = 0\) \({x^2} = 25\) \(x = 5\) hoặc \(x =  - 5\) Vậy phương trình có hai nghiệm \(x = 5\); \(x =  - 5\). b) \({\left( {x + 3} \right)^2} = 5\) \(x + 3 = \sqrt 5 \) hoặc \(x + 3 =  - \sqrt 5 \) \(x =  - 3 + \sqrt 5 \) hoặc \(x =  - 3 - \sqrt 5 \)

Vậy phương trình có hai nghiệm \(x =  - 3 + \sqrt 5 \); \(x =  - 3 - \sqrt 5 \).

LT4

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 4 trang 13 SGK Toán 9 Kết nối tri thức

Cho phương trình \({x^2} + 6x = 1\). Hãy cộng vào cả hai vế của phương trình với cùng một số thích hợp để được một phương trình mà vế trái có thể biến đổi thành một bình phương. Từ đó, giải phương trình đã cho.

Phương pháp giải:

Các bước giải phương trình: + Bước 1: Cộng thêm 9 vào 2 vế để đưa phương trình về dạng: \({A^2} = B\left( {B \ge 0} \right)\). + Bước 2: Nếu \({A^2} = B\left( {B \ge 0} \right)\) thì \(A = \sqrt B \) hoặc \(A =  - \sqrt B \). Giải các phương trình đó và kết luận.

Lời giải chi tiết:

\({x^2} + 6x = 1\) \({x^2} + 2.x.3 + {3^2} = 1 + 9\) \({\left( {x + 3} \right)^2} = 10\) \(x + 3 = \sqrt {10} \) hoặc \(x + 3 =  - \sqrt {10} \) \(x =  - 3 + \sqrt {10} \)       \(x =  - 3 - \sqrt {10} \) Vậy phương trình có hai nghiệm \(x =  - 3 + \sqrt {10} \); \(x =  - 3 - \sqrt {10} \).

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