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Giải bài 3 trang 72 sách bài tập toán 9 - Kết nối tri thức tập 2

a) Giải bất phương trình ( - 10x + 7 > 3x - 4). b) Chứng minh rằng (9{a^2} - 6a ge - 1) với mọi số thực a.

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

Toán - Văn - Anh
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Đề bài

a) Giải bất phương trình \( - 10x + 7 > 3x - 4\). b) Chứng minh rằng \(9{a^2} - 6a \ge  - 1\) với mọi số thực a.

Phương pháp giải - Xem chi tiết

a) + Đưa bất phương trình về dạng bất phương trình bậc nhất một ẩn \(ax + b < 0\left( {a \ne 0} \right)\). + Bất phương trình \(ax + b < 0\left( {a \ne 0} \right)\) được giải như sau: \(ax + b < 0\) \(ax <  - b\) Nếu \(a > 0\) thì \(x <  - \frac{b}{a}\). Nếu \(a < 0\) thì \(x >  - \frac{b}{a}\). b) Chứng minh \(9{a^2} - 6a + 1 \ge 0\) với mọi số thực a, suy ra \(9{a^2} - 6a \ge  - 1\) với mọi số thực a.

Lời giải chi tiết

a) \( - 10x + 7 > 3x - 4\) \(3x + 10x < 7 + 4\) \(13x < 11\) \(x < \frac{{11}}{{13}}\) Vậy bất phương trình có nghiệm \(x < \frac{{11}}{{13}}\). b) Ta có: \(9{a^2} - 6a + 1 = {\left( {3a} \right)^2} - 2.3a + 1 = {\left( {3a - 1} \right)^2} \ge 0\) với mọi số thực a. Do đó, \(9{a^2} - 6a \ge  - 1\) với mọi số thực a.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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