Giải bài tập SGK toán lớp 9, tập 2, Bài 3. Phương trình bậc hai một ẩn

Bài 11 trang 42

Đưa các phương trình sau về dạng ax2+bx+c=0$\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">a</span></span>}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">b</span></span>}\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">c</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">=</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">0</span></span>}$ và chỉ rõ các hệ số a,b,c$\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">a</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">,</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">b</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">,</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">c</span></span>}$:

a) 5x2+2x=4−x$\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">5</span></span>}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">=</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">4</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">-</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}$             

b) 35x2+2x−7=3x+12$\frac{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">3</span></span>}}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">5</span></span>}}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">-</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">7</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">=</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">3</span></span>}\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\frac{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">1</span></span>}}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}$

c) 2x2+x−√3=√3x+1$\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">-</span></span>\sqrt{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">3</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">=</span></span>\sqrt{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">3</span></span>}}\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">1</span></span>}$;              

d) 2x2+m2=2(m−1)x$\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">+</span></span>{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">m</span></span>}}^{\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">=</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">2</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">(</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">m</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">-</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">1</span></span>}<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">)</span></span>\mathrm{<span\; style="font-size:16px;"><span\; style="font-family:arial,helvetica,sans-serif;">x</span></span>}$, m$$m là một hằng số.

Lời giải chi tiết

Bài 12 (trang 42 SGK Toán 9 tập 2): Giải các phương trình sau:

Lời giải

Bài 13 (trang 43 SGK Toán 9 tập 2): Cho các phương trình:

Hãy cộng vào hai vế của mỗi phương trình cùng một số thích hợp để được một phương trình mà vế trái thành một bình phương.

Lời giải

Bài 14 (trang 43 SGK Toán 9 tập 2): Hãy giải phương trình : 2x2 + 5x + 2 = 0 theo các bước như ví dụ 3 trong bài học.

Lời giải