a.Xét tgiac ADB và tgiac ACI có:

góc BAD = góc IAC(gt)

góc BDA= góc ICA(gt)

Vậy tgiac ADB đồng dạng với tgiac ACI(g.g)

=> góc ABD = góc AIC => góc ABD = góc DIC 

b.xét tgiac ADB và tgiac CDI có:

góc ADB= góc CDI(đối đỉnh)

góc ABD= góc CID(cmt)

vậy tgiac ADB đồng dạng với tgiac CDI(g.g)

\(\frac{1}{10}\)+\(\frac{1}{40}\)+\(\frac{1}{88}\)+\(\frac{1}{154}\)+\(\frac{1}{238}\)+\(\frac{1}{340}\)

=\(\frac{1}{2.5}\)+\(\frac{1}{5.8}\)+\(\frac{1}{8.11}\)+\(\frac{1}{11.14}\)+\(\frac{1}{14.17}\)+\(\frac{1}{17.20}\)

=\(\frac{1}{3}\)(\(\frac{3}{2.5}\)+\(\frac{3}{5.8}\)+\(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+\(\frac{3}{14.17}\)+\(\frac{3}{17.20}\))

=\(\frac{1}{3}\)(\(\frac{1}{2}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{8}\)+\(\frac{1}{8}\)-\(\frac{1}{11}\)+\(\frac{1}{11}\)-\(\frac{1}{14}\)+\(\frac{1}{14}\)-\(\frac{1}{17}\)+\(\frac{1}{17}\)-\(\frac{1}{20}\))

=\(\frac{1}{3}\)(\(\frac{1}{2}\)-\(\frac{1}{20}\))

=\(\frac{1}{3}\).\(\frac{9}{20}\)

=\(\frac{3}{20}\)

Vì a,b,c là độ dài 3 cạnh của 1 tam giác nên ta có

a+b-c>0; b+c-a>0; b+c-a>0

áp dụng BĐT \(\frac{1}{x}\)+\(\frac{1}{y}\)\(\ge\)\(\frac{4}{x+y}\) ta có:

\(\frac{1}{a+b-c}\)+\(\frac{1}{b+c-a}\)=\(\ge\)\(\frac{4}{a+b-c+b+c-a}\)=\(\frac{4}{2b}\)=\(\frac{2}{b}\)(1)

\(\frac{1}{a+b-c}\)+\(\frac{1}{c+a-b}\)\(\ge\)\(\frac{4}{a+b-c+c+a-b}\)=\(\frac{4}{2a}\)=\(\frac{2}{a}\)(2)

\(\frac{1}{b+c-a}\)+\(\frac{1}{c+a-b}\)\(\ge\)\(\frac{4}{b+c-a+c+a-b}\)=\(\frac{4}{2c}\)=\(\frac{2}{c}\)(3)

cộng vế với vế của(1);(2) và (3) ta có:

\(\frac{2}{a+b-c}\)+\(\frac{2}{b+c-a}\)+\(\frac{2}{c+a-b}\)\(\ge\)\(\frac{2}{b}\)+\(\frac{2}{a}\)+\(\frac{2}{c}\)

<=>\(\frac{1}{a+b-c}\)+\(\frac{1}{b+c-a}\)+\(\frac{1}{c+a-b}\)\(\ge\)\(\frac{1}{a}\)+\(\frac{1}{b}\)+\(\frac{1}{c}\)

dấu = xảy ra khi a=b=c

IV. Rewrite the sentence so that the meaning doesn’t change: (3pts)

1. Do you mind if I open the windows?

=> Would you mind if I opened the windows?

2. “Is the Great Wall in China?” She asked me.

=> She asked me if the Great Wall was in China.

3. All of you must do this test carefully.

=> This test must be done carefully.

4. She asked him: “ Will you stay with your friends tomorrow?”

=> She asked him if he would stay with his friends the day after.

5. To go swimming is interesting.

=> It’s interesting to go swimming.

III. Put the correct form of the verb/ word in brakets: (2pts)

1.     The lights went out when we (watch) …were watching… television.

2.     Would you mind if I (carry) …carried… your luggage?

3.     The boy (sit) ……sitting…… next to me was very nervous.

4.     (you/ finish) ……Have you finished …… your homework yet, Ba?

5.     Nga asked Ba if he (go) ……went… to Sapa by train that day.

6.     Do you mind (help) ........helping..... me to do this exercise?

7.     Every week, there are two  (fly) ……flights......from Ha Noi to Nha Trang.   

8.     I spent my (child)........childhood.....  in the country.

đáy nhân chiều cao rồi chia cho 2

A= \(\frac{n+3}{n-2}\)=\(\frac{\left(n-2\right)+5}{n-2}\)=1+\(\frac{5}{n-2}\)

Để A là phân số tối giản khi n-2 \(\pm\) Ư(5)

Vậy n-2\(\pm\)5k

<=> n\(\pm\)5h+2

(2\(x^4\)+2\(x^2\)\(y^2\)) +(\(x^2\)\(y^2\)+\(y^4\))+2\(y^2\)

=(2.\(x^2\).\(x^2\)+2\(x^2\).\(y^2\))+(\(x^2\).\(y^2\)+\(y^2\).\(y^2\))+2\(y^2\)

=2\(x^2\).(\(x^2\)+\(y^2\))+\(y^2\).(\(x^2\)+\(y^2\))+2\(y^2\)

\(\frac{1}{x}\)+\(\frac{1}{y}\)=\(\frac{1}{24}\)<=>\(\frac{24y}{24xy}\)+\(\frac{24x}{24xy}\)=\(\frac{xy}{24xy}\)

<=> 24y +24x=xy<=> (24y-xy) -(576-24x)+576=0

<=> y(24-x) -24(24-x)=-576

<=> (24-x)(y-24)=-576=-576.1=1.(-576)=(-24).24=24.(-24)=12.(-48)=48.(-12)=....

và lần lượt cho 24-x và y-24 = các kết quả kia và chỉ lấy những giá trị là số tự nhiên