kmjkjpjpi

mình quên ĐK là x,y,z dương

6, \(\sqrt{xy}+2\sqrt{x}-3\sqrt{y}-6=\sqrt{x}\left(\sqrt{y}+2\right)-3\left(\sqrt{y}+2\right)=\left(\sqrt{x}-3\right)\left(\sqrt{y}+2\right)\)

7, \(7+2\sqrt{10}=7+2\sqrt{5.2}=5+2\sqrt{5.2}+2=\left(\sqrt{5}+\sqrt{2}\right)^2\)

8, \(5-2\sqrt{6}=5-2\sqrt{2.3}=3-2\sqrt{2.3}+2=\left(\sqrt{3}-\sqrt{2}\right)^2\)

9, \(\sqrt{x^2-y^2}-x+y=\sqrt{\left(x-y\right)\left(x+y\right)}-\left(x-y\right)\)

\(=\sqrt{x-y}\left(\sqrt{x+y}-\sqrt{x-y}\right)\)

10, \(3x-2\sqrt{x}=\sqrt{x}\left(3\sqrt{x}-2\right)\)

1, \(\sqrt{xy}-x=\sqrt{x}\left(\sqrt{y}-\sqrt{x}\right)\)

2, \(x+y-2\sqrt{xy}=\left(\sqrt{x}-\sqrt{y}\right)^2\)

3, \(x\sqrt{y}-y\sqrt{x}=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)

4, \(2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}=2\sqrt{5}\left(1-\sqrt{2}\right)-\sqrt{3}\left(1-\sqrt{2}\right)\)

\(=\left(2\sqrt{5}-\sqrt{3}\right)\left(1-\sqrt{2}\right)\)

5, \(\sqrt{35}-\sqrt{14}=\sqrt{7}\left(\sqrt{5}-\sqrt{2}\right)\)

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

\(=2-x\cdot\frac{x-1}{x-2}=\frac{2x-4}{x-2}-\frac{x^2-x}{x-2}=\frac{-x^2+3x-4}{x-2}\)

\(B=\frac{2\sqrt{5}x}{x-2}\cdot\left|x-2\right|+\frac{3\sqrt{5}x^2}{x}=\frac{2\sqrt{5}x}{x-2}\cdot\left|x-2\right|+3\sqrt{5}x\)

Với 0 < x < 2 \(B=-2\sqrt{5}x+3\sqrt{5}x=\sqrt{5}x\)

Với x > 2 \(B=2\sqrt{5}x+3\sqrt{5}x=5\sqrt{5}x\)

\(C=\frac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\sqrt{x}\left(\sqrt{x}+5\right)}+\sqrt{\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-5\right)^2}}=\frac{\sqrt{x}-5}{\sqrt{x}}+\left|\frac{\sqrt{x}-1}{\sqrt{x}-5}\right|\)

Với 0 < x < 1 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}+\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}+\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{2x-11\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)

Với 1 < x < 5 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}-\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}-\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{-9\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)

Với x > 5 \(C=\frac{\sqrt{x}-5}{\sqrt{x}}+\frac{\sqrt{x}-1}{\sqrt{x}-5}=\frac{x-10\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}+\frac{x-\sqrt{x}}{x\left(\sqrt{x}-5\right)}=\frac{2x-11\sqrt{x}+25}{x\left(\sqrt{x}-5\right)}\)

I.       Find the one choice that best completes the sentence.

1.      “Where was Michael Caine born?” “In Britain, but today he _____ in the United States.”

a. has lived                    b. live                                c. lives                               d. lived

2.      Have they found a malaria vaccine _____?

a. already                      b. yet                                 c. since                              d. for

3.      “We’re still looking for Thomas.” “Hasn’t he _____ yet?”

a. been found                b. be found                        c. been founded                d. be founded

4.      “Whatever happened to that fortune-teller?”

“I don’t know. She _____ around here in a long time.”

a. hasn’t been saw        b. didn’t see                      c. hasn’t been seeing         d. hasn’t been seen

5.      “Diana is a wonderful ballet dancer.” “She _____ since she was four.”

a. has been dancing      b. has been danced           c. is dancing                      d. was danced

6.      “What a beautiful dress you’re wearing!”

“Thank you. It _____ especially for me by a French tailor.”

a. is made                     b. has made                       c. made                              d. was made

7.      “Those eggs of different colors are very artis.” “Yes, they _____ in Russia.”

a. were painted             b. were paint                     c. were painting                 d. painted

8.      The city still bears the French name _____ Aix-la-Chapelle.

a. of                              b. as                                   c. is                                    d. for

9.      The work of designer Sonia Rykiel was the original inspiration _____ the movie.

a. of                              b. for                                 c. to                                   d. in

10.  Wearing uniforms helps poor students feel equal _____ others.

a. of                              b. for                                 c. to                                   d. with

11.  We sell a selection of plain and _____ ties.

a. pattern                       b. patterned                       c. patterning                      d. patterns

12.  She teaches _____.

a. poet                           b. poem                             c. poets                              d. poetry

13.  There is friendly _____ between the two teams.

a. rival                           b. rivals                              c. relativity                        d. rivalry

14.  We hope to increase _____ this year to $50 million.

a. sale                            b. sells                               c. salable                            d. selling

15.  It seems the most logical solution _____ the problem.

a. of                              b. to                                   c. with                               d. from

1. C

2. B

3. A

4. D

5. B

6. D

7. A

8. C

9. D

10. C

11. A

12. D

13. A

14. A

15. B

Tham khảo !
a + b)

c )

chia hình vuông thành 25 hình vuông nhỏ có cạnh bằng 1cm ( nghĩa là diện tích bằng 1cm^2)

Theo nguyên lí dirichlet  do có 51 điểm và 25 hình vuông

nên tồn tại một hình vuông con chứa ít nhất 3 điểm

Nên 3 điểm đỏ taoh thành 1 tma giác có diện tích nhỏ hơn 1/2 diện tích hình vuông nhỏ là 0,5 cm^2

Vậy ta có điều phải chứng minh