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ĐKXĐ: \(\left[{}\begin{matrix}x\ge\dfrac{\sqrt{7}+4}{2}\\x\le\dfrac{-\sqrt{7}-4}{2}\end{matrix}\right.\)

phương trình tương đương

\(\left(1-3x\right)^2+\left(x-1\right)=\left(2-x\right)\sqrt{\left(2-x\right)\left(1-3x\right)-\left(x-1\right)}\) (1)

Đặt \(\left\{{}\begin{matrix}u=1-3x\\v=\sqrt{\left(2-x\right)\left(1-3x\right)-\left(x-1\right)}\end{matrix}\right.\)

từ (1) ta có

\(u^2=\left(2-x\right)v-\left(x-1\right)\)

\(\Rightarrow\left\{{}\begin{matrix}u^2=\left(2-x\right)v-\left(x-1\right)\\v^2=\left(2-x\right)u-\left(x-1\right)\end{matrix}\right.\)

lấy hai phương trình trên trừ vế theo vế ta được

\(\left(u-v\right)\left(u+v\right)+\left(2-x\right)\left(u-v\right)=0\)

\(\Leftrightarrow\left(u-v\right)\left(u+v+2-x\right)=0\)

Với \(u=v\Rightarrow1-3x=\sqrt{3x^2-8x+3}\)=> x=......

với \(v=x-2-u\Rightarrow\sqrt{3x^2-8x+3}=3x^2-3\)\(\Rightarrow x=...\)

Đây không phải bài lớp 8 bạn nhé!

Rewrite the sentences without changing their meaning. Use the words in brackets.

3. Sebastien is a French, but he plays Vietnamese folk games well. (although)

=> Although Sebastien is a French, he plays Vietnamese folk games well.

4. He has to join the festival in order to play Vietnamese folk games. (so)

=> He has to join the festival so as to play Vietnamese folk games.

5. Although the weather was terrible, we had a good time. (spite)

=> We had a good time in spite of the terrible weather.

6. So that Susan would be fit for the skiing, she went to the gym three times a week. (order)

=> Susan went to the gym three times a week in order to be fit for the skiing.

7. My family went to Huong Pagoda Festival two months ago. (since)

=> It is two months since my family last went to Huong Pagoda Festival.

8. You won’t get in to see the show if you don’t have reserved seats. (unless)

=> You won’t get in to see the show unless you have reserved seats.

Áp dụng công thức \(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{\left(a+b\right)^2}}=\frac{1}{a}+\frac{1}{b}-\frac{1}{a+b}\) vào biểu thức \(B=\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+...+\sqrt{1+\frac{1}{99^2}+\frac{1}{100^2}}\), ta được:

\(B=1+\frac{1}{1}-\frac{1}{2}+1+\frac{1}{2}-\frac{1}{3}+1+\frac{1}{3}-\frac{1}{4}+...+1+\frac{1}{99}-\frac{1}{100}\)

\(=100-\frac{1}{100}=\frac{9999}{100}\)

1. She was late for the interview because she was ________ in traffic for over an hour.

A. stuck B. busy C. slow D. lost

A= x\(^2\) - 2x +5\(=x^2-2\cdot x\cdot1+1+4=\left(x-1\right)^2+4\)

B= 4x\(^2\) + 4x - 5\(=\left(2x\right)^2+2\cdot2x\cdot1+1-6=\left(2x+1\right)^2-6\)

C= x\(^2\) - 8x + 17\(=x^2-2\cdot x\cdot4+16+1=\left(x-4\right)^2+1\)

D= 9x\(^2\) + 6x - 2\(=\left(3x\right)^2+2\cdot3x\cdot1+1-3=\left(3x+1\right)^2-3\)

a) \(3x^2-8x+4=\left(x-2\right)\left(3x-2\right)\)

b) \(3x^2-16x+5=\left(x-5\right)\left(3x-1\right)\)

c) \(2x^2-5x-12=\left(x-4\right)\left(3x+2\right)\)

d) \(8x^2+30x+7=\left(4x+1\right)\left(2x+7\right)\)

e) \(6x^2-7x-20=\left(2x-5\right)\left(3x+4\right)\)

Mấy cái này bấm máy nhanh không í mà

a, \(3x^2-8x+4=3x^2-6x-2x+4\)

\(=3x.\left(x-2\right)-2.\left(x-2\right)=\left(x-2\right).\left(3x-2\right)\)

b, \(3x^2-16x+5=3x^2-15x-x+5\)

\(=3x.\left(x-5\right)-\left(x-5\right)=\left(x-5\right).\left(3x-1\right)\)

c, \(2x^2-5x-12=2x^2-8x+3x-12\)

\(=2x.\left(x-4\right)+3.\left(x-4\right)=\left(x-4\right).\left(2x+3\right)\)

d, \(8x^2+30x+7=8x^2+2x+28x+7\)

\(=2x.\left(4x+1\right)+7.\left(4x+1\right)=\left(4x-1\right).\left(2x+7\right)\)

e, \(6x^2-7x-20=6x^2-15x+8x-20\)

\(=3x.\left(2x-5\right)+4x.\left(2x-5\right)=\left(2x-5\right).\left(3x+4x\right)\)

Chúc bạn học tốt!!!