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1 tháng 1 2022

A

~HT~=>

1 tháng 1 2022

A nha bn

51.) It looks better .......... a distance.a.) to                    b.) for                                     c.) at                                      d.) but                                    52.) She was engaged .......... him for ten months before they got married.a.) to                    b.) with                                    c.) for                                     d.) by                                     53.) What did Mr. Brown die ..........?a.) with                 b.)...
Đọc tiếp

51.) It looks better .......... a distance.

a.) to                    b.) for                                     c.) at                                      d.) but                                    

52.) She was engaged .......... him for ten months before they got married.

a.) to                    b.) with                                    c.) for                                     d.) by                                     

53.) What did Mr. Brown die ..........?

a.) with                 b.) by                                      c.) in                                      d.) of                                     

54.) She took me .......... my brother.

a.) by             b.) for                                     c.) to                                      d.) with                                   

55.) It is .......... three o'clock; it is nearly a quarter past three.

a.) about         b.) at                                      c.) past                                    d.) around                                 

56.) She gave some advice .......... her brother.

a.) to                b.) for                                     c.) with                           d.) all are correct                        

57.) He was brought .......... the judge.

a.) to                b.) with                                    c.) before                                  d.) for                                    

58.) The government must care .......... the families of invalid soldiers.

a.) about              b.) for                                     c.) to                                      d.) at                                     

59.) They like to sit .......... the fire.

a.) by                   b.) on                                      c.) for                                    d.) with                                   

60.) I cannot do it .......... you.

a.) as                  b.) like                                    c.) by                                      d.) through                              

61.) .......... one enemy he has 50 friends.

a.) With             b.) To                                      c.) For                                 d.) Through                                

62.) Mary married a wealthy man. She got married .......... him last June.

a.) by                 b.) for                                     c.) about                                  d.) to                                     

63.) There were .......... 100 people at the meeting.

a.) up               b.) on                                      c.) upon                                 d.) above                                  

64.) William is big .......... his age.

a.) with              b.) for                                     c.) by                                    d.) through                                

65.) The god jumped .......... the table.

a.) through          b.) over                                    c.) out of                              d.) past                                   

66.) He didn't dare to say it .......... my face.

a.) on                  b.) with                                    c.) in                                      d.) to                                     

67.) .......... general, that is true. However, there are many exceptions.

a.) On                b.) In                                      c.) By                                  d.) Through                                

68.) Can you recommend me a good book .......... life in the sixteenth century?

a.) of                  b.) about                                   c.) in                                    d.) from                                   

1
31 tháng 12 2021

dịch gg dịch nha bn !

1 tháng 1 2022

Ta có: \(a^3+b^3=2021c^3\)\(\Leftrightarrow a^3+b^3+c^3=2022c^3\)

Mà \(2022⋮3\)\(\Rightarrow2022c^3⋮3\)\(\Rightarrow a^3+b^3+c^3⋮3\)

Mặt khác \(\left(a^3+b^3+c^3\right)-\left(a+b+c\right)\)\(=\left(a^3-a\right)+\left(b^3-b\right)+\left(c^3-c\right)\)

\(=a\left(a^2-1\right)+b\left(b^2-1\right)+c\left(c^2-1\right)\)

\(=a\left(a-1\right)\left(a+1\right)+b\left(b-1\right)\left(b+1\right)+c\left(c-1\right)\left(c+1\right)\)

Vì \(a,a-1,a+1\)là 3 số liên tiếp nên trong 3 số này luôn tồn tại một bội của 3

\(\Rightarrow a\left(a-1\right)\left(a+1\right)⋮3\)

Tương tự, ta cũng có \(b\left(b-1\right)\left(b+1\right)⋮3\)và \(c\left(c-1\right)\left(c+1\right)⋮3\)

\(\Rightarrow a\left(a-1\right)\left(a+1\right)+b\left(b-1\right)\left(b+1\right)+c\left(c-1\right)\left(c+1\right)⋮3\)

\(\Rightarrow\left(a^3+b^3+c^3\right)-\left(a+b+c\right)⋮3\)

Mà \(a^3+b^3+c^3⋮3\left(cmt\right)\)\(\Rightarrow a+b+c⋮3\left(đpcm\right)\)

1 tháng 1 2022

Answer:

Bài 2 mình không biết làm, bạn thông cảm ạ.

Bài 3:

P đạt giá trị nguyên khi \(3⋮\sqrt{x}-2\)

\(\Rightarrow\sqrt{x}-2\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Rightarrow\sqrt{x}=\left\{1;3;5\right\}\)

\(\Rightarrow x=\left\{1;9;25\right\}\)

Tl : 103.779
31 tháng 12 2021

14256 + 89523 = 103779

31 tháng 12 2021

đợi tý đang tính

31 tháng 12 2021

Điều kiện \(x,y\ne-1\)

Xét phương trình thứ hai: 

\(xy+x+y=3\)\(\Leftrightarrow xy+x+y+1=4\)\(\Leftrightarrow x\left(y+1\right)+\left(y+1\right)=4\)\(\Leftrightarrow\left(x+1\right)\left(y+1\right)=4\)

Như vậy hệ đã cho \(\Leftrightarrow\hept{\begin{cases}\frac{1}{x+1}+\frac{1}{y+1}=1\\\left(x+1\right)\left(y+1\right)=4\end{cases}}\)(*)

Đặt \(\hept{\begin{cases}x+1=a\\y+1=b\end{cases}\left(a,b\ne0\right)}\), lúc này (*) \(\Leftrightarrow\hept{\begin{cases}\frac{1}{a}+\frac{1}{b}=1\\ab=4\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{a+b}{ab}=1\\ab=4\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{a+b}{4}=1\\b=\frac{4}{a}\end{cases}}\Leftrightarrow\hept{\begin{cases}a+\frac{4}{a}=4\left(1\right)\\b=\frac{4}{a}\left(2\right)\end{cases}}\)

Giải phương trình \(\left(1\right)\), ta có: \(a+\frac{4}{a}=4\)\(\Leftrightarrow\left(\sqrt{a}\right)^2-2.\sqrt{a}.\frac{2}{\sqrt{a}}+\left(\frac{2}{\sqrt{a}}\right)^2=0\)

\(\Leftrightarrow\left(\sqrt{a}-\frac{2}{\sqrt{a}}\right)^2=0\)\(\Leftrightarrow\sqrt{a}-\frac{2}{\sqrt{a}}=0\)\(\Leftrightarrow\sqrt{a}=\frac{2}{\sqrt{a}}\)\(\Leftrightarrow\left(\sqrt{a}\right)^2=2\)\(\Leftrightarrow a=2\)(nhận)

Thay vào \(\left(2\right)\), ta có: \(b=\frac{4}{a}=\frac{4}{2}=2\)(nhận)

Như vậy ta có \(a=b=2\)\(\Leftrightarrow x+1=y+1=2\)\(\Leftrightarrow x=y=1\)(nhận)

Vậy hệ đã cho có nghiệm duy nhất (1;1)