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I.  Rewrite the quotations in reported speech. Change the pronouns if necessary.1.     ‘I want to catch the shoplifter,’ the security guard said.………………………………………………………………………………………………………2.     ‘The police arrested a vandal,’ she said.………………………………………………………………………………………………………3.     ‘It’s difficult to catch drug...
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I.  Rewrite the quotations in reported speech. Change the pronouns if necessary.

1.     ‘I want to catch the shoplifter,’ the security guard said.

………………………………………………………………………………………………………

2.     ‘The police arrested a vandal,’ she said.

………………………………………………………………………………………………………

3.     ‘It’s difficult to catch drug dealers,’ said the police inspector.

………………………………………………………………………………………………………

4.     ‘We are questioning two teenagers about the burglary,’ the police officer said.

………………………………………………………………………………………………………

5.     ‘I sometimes go joyriding with my friends,’ he said.

………………………………………………………………………………………………………

6.     ‘The police are looking for the bank robbers,’ she said.

………………………………………………………………………………………………………

7.     ‘A boy in my class vandalized a park bench,’ my brother said.

………………………………………………………………………………………………………

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24 tháng 1 2022

\(P=\left(\frac{1}{x}+\frac{1}{y}\right).\sqrt{1+x^2y^2}\)

\(\rightarrow P>2.\sqrt{\frac{1}{x}.\frac{1}{y}}.\sqrt{1+\left(xy\right)^2}\)

\(\rightarrow P>2.\sqrt{\frac{1}{xy}}.\sqrt{1+\left(xy\right)^2}\)

\(\rightarrow P>2\sqrt{\frac{1}{xy}+xy}\)

Đặt \(xy=t\)

\(\rightarrow P>2\sqrt{\frac{1}{t}+t}\)

Ta có :

\(1>x+y>2\sqrt{xy}\)

\(\rightarrow\sqrt{xy}< \frac{1}{2}\)

\(\rightarrow xy< \frac{1}{4}\)

\(\rightarrow t< \frac{1}{4}\)

Lại có :

\(\frac{1}{t}+t=\frac{15}{16t}+\left(\frac{1}{16}+t\right)\)

\(\rightarrow\frac{1}{t}+t>\frac{15}{16.\frac{1}{4}}+2\sqrt{\frac{1}{16}.t}\)

\(\rightarrow\frac{1}{t}+t>\frac{17}{4}\)

\(\rightarrow B>2.\sqrt{\frac{17}{4}}\)

\(\rightarrow B>\sqrt{17}\)

Dấu bằng xảy ra khi \(x=y=\frac{1}{2}\)