7. B

8. D

9. D

10. A

11. A

12. C

13. B

14. D

15. D

16. C

17. B

18. C

19. A

a. \(Q=\dfrac{a}{\sqrt{a^2-b^2}}-\left(1+\dfrac{a}{\sqrt{a^2-b^2}}\right):\dfrac{b}{a-\sqrt{a^2-b^2}}\)

\(=\dfrac{a}{\sqrt{a^2-b^2}}-\dfrac{a+\sqrt{a^2-b^2}}{\sqrt{a^2-b^2}}.\dfrac{a-\sqrt{a^2-b^2}}{b}\)

\(=\dfrac{a}{\sqrt{a^2-b^2}}-\dfrac{b}{\sqrt{a^2-b^2}}=\dfrac{a-b}{\sqrt{a^2-b^2}}=\dfrac{\sqrt{a-b}}{\sqrt{a+b}}\)

b. Thay \(a=3b\) vào \(Q\), ta được

\(Q=\dfrac{\sqrt{3b-b}}{\sqrt{3b+b}}=\dfrac{\sqrt{2b}}{\sqrt{4b}}=\dfrac{1}{\sqrt{2}}\)

C

a. \(\left(3x-2\right)^2-49=0\)

\(\Leftrightarrow\left(2x-3-7\right)\left(2x-3+7\right)=0\)

\(\Leftrightarrow4\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

b. \(2x\left(x-5\right)-7\left(5-x\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(2x+7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\2x+7=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{7}{2}\end{matrix}\right.\)

c. \(x^2-3x-10=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

Hha lú xí

a. \(x>1\)

b. \(0\le x< 16\)

a. \(\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\)

b. \(\sqrt{\left(0,3\right)^2}=\left|0,3\right|=0,3\)

c. \(\sqrt{\left(-0,3\right)^2}=\left|-0,3\right|=0,3\)

d. \(-0,2\sqrt{\left(-0,5\right)^2}=-0,2\left|-0,5\right|=-0,2.0,5=-0,1\)

Bài 4:

a. \(\sqrt{x}=2\Leftrightarrow x=2^2\Leftrightarrow x=4\)

b. \(\sqrt{x}+1=5\Leftrightarrow\sqrt{x}=4\Leftrightarrow x=16\)

c. \(\sqrt{x-1}+1=4\Leftrightarrow\sqrt{x-1}=3\Leftrightarrow x-1=9\Leftrightarrow x=10\)

d. \(\sqrt{x-1}=\sqrt{3}\Leftrightarrow x-1=3\Leftrightarrow x=4\)

ĐKXĐ: \(2x^2-9\ge0\Leftrightarrow x^2\ge\dfrac{9}{2}\Leftrightarrow x\ge\dfrac{3}{\sqrt{2}}\)

Ta có với mọi \(x\ge\dfrac{3}{\sqrt{2}}\) thì \(\left\{{}\begin{matrix}\sqrt{2x^2-9}\ge0\\-x\le-\dfrac{3}{\sqrt{2}}\end{matrix}\right.\)

\(\Rightarrow\) Phương trình vô nghiệm 

1. They paid for dinner in order to apologize for their behaviour

2. I didn't want to wake the baby so that I walked quietly

3. He locked the door so that the prisoner couldn't escape

4. She tries to learn English with a view to communicating with foreigners

5. She wore dark glasses with a view not to being recognized 
6. She applied for the job with a view to earning more money

7. We left quietly so as not to disturb him

8. Lan tiptoed up the stairs in oder not to wake anyone up

9. He left without saying goodbye so as not to disturb the meeting

10. Mike put on his raincoat in order not to get soaked