Ta có:

\(A=x^6-3x^5+4x^4-3x^3+2x^2-x+1\) 

\(=\left(x^6-3x^5+3x^4-1\right)+\left(x^4-2x^3+x^2\right)+\left(x^2-x\right)+1\)

\(=\left(x^2-x\right)^3+\left(x^2-x\right)^2+\left(x^2-x\right)+1\)

Thay `x^2-x=10` vào A ta có:

\(A=10^3+10^2+10+1=1111\)

A = x⁶ - 3x⁵ + 4x⁴ - 3x³ + 2x² - x + 1

= (x⁶ - x⁵) - 2x⁵ + 2x⁴ + 2x⁴ - 2x³ - x³ + x² + x² - x + 1

= x⁴(x² - x) - 2x³(x² - x) + 2x²(x² - x) - x(x² - x) + (x² - x) + 1

= (x² - x)(x⁴ - 2x³ + 2x² - x) + 1

= 10(x⁴ - x³ - x³ + x² + x² - x) + 1

= 10[x²(x² - x) - x(x² - x) + (x² - x)] + 1

= 10(x² - x)(x² - x + 1) + 1

= 10.10.(10 + 1) + 1

= 100.11 + 1

= 1100 + 1

= 1101

1. She wants to have the party on Saturday.

2. They have the party at her grandmother's house. Because her grandmother's house is bigger than her house.

3. It's thirty-one, in Regent Street.

4. They hold the party at half past four.

5. The girl asks her friends to bring cakes and some games.

6. The man asks her friends to wear jeans.

7. They can play in the garden if the weather is nice.

8. The man asks her friends parents to phone him.

\(x^4+6x^3+7x^2-6x+1\)

\(=x^4+9x^2+1+6x^3-2x^2-6x\)

\(=\left(x^2\right)^2+\left(3x\right)^2+\left(-1\right)^2+2\cdot x^2\cdot3x+2\cdot x^2\cdot\left(-1\right)+2\cdot3x\cdot\left(-1\right)\)

\(=\left(x^2+3x-1\right)^2\)

---------------------

Áp dụng hằng đẳng thức: \(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2ac+2bc\)

Trong trường hợp này `a=x^2; b=3x; c=-1` 

20.

a) \(A=4x^2-4x+m\)

\(=4x^2-4x+1-1+m\)

\(=\left(4x^2+4x+1\right)+\left(m-1\right)\)

\(=\left(2x+1\right)^2+\left(m-1\right)\)

Để biếu thức không âm thì \(A\ge0\Rightarrow\left(2x+1\right)^2+\left(m-1\right)\ge0\)

Mà: \(\left(2x+1\right)^2\ge0\)

\(\Rightarrow\) Để \(A\ge0\Rightarrow m-1\ge0\Leftrightarrow m\ge1\) 

b) \(B=x^2-6x+2-m\)

\(=x^2-6x+9-9+2-m\)

\(=\left(x^2+6x+9\right)+\left(2-m-9\right)\)

\(=\left(x+3\right)^2+\left(-m-7\right)\)

Để bt không âm thì \(B\ge0\Rightarrow\left(x+3\right)^2+\left(-m-7\right)\ge0\)

Mà: \(\left(x+3\right)^2\ge0\)

⇒ Để \(B\ge0\Rightarrow-m-7\ge0\Leftrightarrow-m\ge7\Leftrightarrow m\le-7\) 

Câu 16:

a) Số chính phương lẻ có dạng: \(\left(2x+1\right)^2=4x^2+4x+1=4x\left(x+1\right)+1\) 

Vì \(x\in N\Rightarrow x\left(x+1\right)\) là tích của 2 số tự nhiên liên tiếp

\(\Rightarrow x\left(x+1\right)\) ⋮ 2 

\(\Rightarrow4x\left(x+1\right)\) ⋮ 8

\(\Rightarrow4x\left(x+1\right)+1\) chia 8 dư 1 

b)  Theo câu a ta biết số chính phương lẻ chia 8 sẽ dư 1 mà `1^2;3^2;5^2;7^2;...;2023^2` đều là các số tự nhiên lẻ ⇒ Chúng đều chia 8 dư 1 

Từ 1 đến 2023 có số lượng số lẻ là: \(\left(2023-1\right):2+1=1012\) (số) 

Khi đó `1^2+3^2+5^2+...+2023^2` chia 8 dư `1*1012=1012` 

Mà: 1012 chia 8 dư 4 ⇒ Tổng `1^2+3^2+5^2+...+2023^2` chia 8 dư 4 

\(a^3+4a^2-29a+24\)

\(=a^3-a^2+5a^2-5a-24a+24\)

\(=a^2\left(a-1\right)+5a\left(a-1\right)-24\left(a-1\right)\)

\(=\left(a-1\right)\left(a^2+5a-24\right)\)

\(=\left(a-1\right)\left(a^2-3a+8a-24\right)\)

\(=\left(a-1\right)\left[a\left(a-3\right)+8\left(a-3\right)\right]\)

\(=\left(a-1\right)\left(a-3\right)\left(a+8\right)\)

đề sai rồi nha viết lại nhé 

`#3107.101107`

Ta có: `\sqrt{50} + \sqrt{65} - \sqrt{16} > \sqrt{49} + \sqrt{64} - \sqrt{16} = 7 + 8 + 4 = 19`

Mà `\sqrt{120} < \sqrt{361} (= 19)`

`\Rightarrow \sqrt{50} + \sqrt{65} - \sqrt{16} > \sqrt{120}`

@Phạm Lê Minh Vương cái đó không phải chép mạng nhé!Cái đó là kí tên thôi!

\(#\text{7064681}\)

+ ed: prayed, called, missed, enjoyed, looked

+ d: closed, loved, danced, phoned, lived

-y ➙ ied: studied, cried, tidied, tried, carried

double consonant + ed: travelled, stopped, robbed, dropped, referred

+ed: laughed, prayed, called, missed, enjoyed, looked

+d: closed, loved, danced, phoned, lived

y => ied: studied, cried, tidied, tried, carried

còn lại: stopped, robbed, dropped, referred, travelled

2 Did the Emperor of Spain give him fifteen ships
3 Did they leave Spain in 1619
4 Was the journey long and dangerous
5 Did Magellan discover the Pacific Ocean
6 Did Magellan die with soldiers in battle
7 Did a Spanish sailor complete the voyage
8 Did the remaining ship reach Spain in 1522