I think it will rain next Sunday

Will rain

1.She goes to English class twice a week.

=>How often does she go to English class?

2.She is into listening to music.

=>She enjoys listening to music.

3.She asked, "Don't play football on the road, Nam."

=>She asked Nam not to play football on the road.

4.They asked me, "Leave your keys outside."

=>They asked me to leave my keys outside.

5.Lan prefers swimming to playing badminton.

=>Lan likes swimming more than playing badminton.

6.She is a faster runner than I am.

=>She runs faster than I do.

Word form:

The villagers often wear traditional clothes on special occasions.

Luckily,They are alive after an accident

`#\text{nn}`

`1,`

`1)`

\(\left(3x-1\right)^2\\ =\left(3x\right)^2-2\cdot3x\cdot1+1^2\\ =9x^2-6x+1\)

`2)`

\(\left(2y+3x\right)^2\\ =\left(2y\right)^2+2\cdot2y\cdot3x+\left(3x\right)^2\\ =4y^2+12xy+9x^2\)

`3)`

\(\left(4x-5\right)^2\\ =16x^2-40x+25\)

`4)`

\(4y^2-9\\ =\left(2y\right)^2-3^2\\ =\left(2y-3\right)\left(2y+3\right)\)

`5)`

\(64x^2-25y^2\\ =\left(8x^2\right)-\left(5y\right)^2\\ =\left(8x-5y\right)\left(8x+5y\right)\)

`6)`

\(\left(2x^3-1\right)^2\\ =\left(2x^3\right)^2-2\cdot2x^3\cdot1+1^2\\ =8x^6-4x^3+1\)

`7)`

\(\left(5xy+7\right)^2\\ =\left(5xy\right)^2+2\cdot5xy\cdot7+7^2\\ =25x^2y^2+70xy+49\)

`8)`

\(\left(3x+8ay^2\right)^2\\ =\left(3x\right)^2+2\cdot3x\cdot8ay^2+\left(8ay^2\right)^2\\ =9x^2+48xay^2+64a^2y^4\)

`9)`

\(\left(a+b\right)^2-\left(a-b\right)^2\\ =\left(a+b-a+b\right)\left(a+b+a-b\right)\\ =2b\cdot2a\\ =4ab\)

`10)`

\(84^2-16^2\\ =\left(84-16\right)\left(84+16\right)\\ =68\cdot100\\ =6800\)

`11)`

\(\left(3xy-z\right)\left(3xy+z\right)\\ =\left(3xy\right)^2-z^2\\ =9x^2y^2-z^2\)

`12)`

\(\left(x^2+5\right)\left(5-x^2\right)\\ =\left(5+x^2\right)\left(5-x^2\right)\\ =5^2-\left(x^2\right)^2\\ =25-x^4\)

`2,`

`1)`

`4x^2 - 12x + 9`

`= (2x)^2 - 2*2x*3 + 3^2`

`= (2x - 3)^2`

`2)`

`36x^2 + 24xy + 4y^2`

`= (6x)^2 + 2*6x*2y (2y)^2`

`= (6x + 2y)^2`

`3)`

`9x^2y^2 - 2xy^2 + 1/9y^2`

`= (3xy)^2 - 2*3xy*1/3y + (1/3y)^2`

`= (3xy - 1/3y)^2`

`4)`

`25x^4 + 10x^2y^3 + y^6`

`= (5x^2)^2 + 2*5x^2*y^3 + (y^3)^2`

`= (5x^2 + y^3)^2`

___

2 HĐT được sử dụng: 

`@` `(A + B)^2 = A^2 + 2AB + B^2`

`@` `(A - B)^2 = A^2 - 2AB + B^2`

`ax^4+bx^4+1`

`=(a+b)x^4+1` 

Vì `ax^4+bx^4+1 \vdots (x-1)^2`

nên `x=1` là nghiệm của đa thức `ax^4+bx^4+1` (định lí Bơ-du)

Khi đó: `(a+b).1^4+1=0`

`=>a+b=-1` (1)

Mà `a=1;b=-2` thoả mãn (1) nên ta được `a=1;b=-2`

P/s: Đề này hơi khó hiểu nha, do `a+b=-1` sẽ có vô số giá trị của a, b thoả mãn nên mình thấy yêu cầu này hơi lạ :v

Xét ΔOAB có OA+OB>AB

Xét ΔOCD có OC+OD>CD

OA+OB+OC+OD=AC+BD>AB+CD

Xét \(\Delta\) IDC vuông tại I có:

\(\widehat{IDC}+\widehat{ICD}=180^o-\widehat{DIC}=180^o-90^o=90^o\)

mà \(\widehat{D}=2\widehat{IDC}\);\(\widehat{C}=2\widehat{ICD}\)

\(\Rightarrow\widehat{C}+\widehat{D}=2\left(\widehat{IDC}+\widehat{ICD}\right)=2\cdot90^o=180^o\)

Vì Δ`IDC` là tam giác vuông

`=> `\(\widehat{D}+\widehat{C}=90^0\)(2 góc nhon phụ nhau)

Có :`DI` là phân giác \(\widehat{ADC}\)(gt)

`=> `\(\widehat{ADI}=\widehat{IDC}=\dfrac{1}{2}\widehat{ADC}\)

`=>`\(\widehat{D}=2\widehat{IDC}\)  `(1)

 Lại có : `CI` Là phân giác\(\widehat{C}\)(gt)`

`=>`\(\widehat{BCI}=\widehat{ICD}=\dfrac{1}{2}\widehat{C}\)

`=>` \(\widehat{C}=2\widehat{ICD}\) `(2)`

Cộng `(1)` và `(2)`

\(\widehat{D}+\widehat{C}=2\left(\widehat{ICD}+\widehat{IDC}\right)\)

`= 2 . 90^0`

`=180^0`