a.

\(a+b+c=0\Rightarrow\left(a+b+c\right)^2=0\)

\(\Rightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)

\(\Rightarrow\left(a^2+b^2+c^2\right)^2=4\left(ab+bc+ca\right)^2\)

\(\Rightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=4\left(a^2b^2+b^2c^2+c^2a^2\right)+8abc\left(a+b+c\right)\)

\(\Rightarrow a^4+b^4+c^4=2\left(a^2b^2+b^2c^2+c^2a^2\right)\)

b.

Từ câu a:

\(a^4+b^4+c^4=2\left(a^2b^2+b^2c^2+c^2a^2\right)\)

\(\Rightarrow2\left(a^4+b^4+c^4\right)=a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)\)

\(\Rightarrow2\left(a^4+b^4+c^4\right)=\left(a^2+b^2+c^2\right)^2\)

\(\Rightarrow a^4+b^4+c^4=\dfrac{\left(a^2+b^2+c^2\right)^2}{2}\)

1. away

2. residence

3. tuition

4. loans

5. sum

6. course

1 away

2 residence 

3 tution

4 loans

5 sum

6 course

 A = (14⁸)²⁰²⁰ + 10 

A =  (14⁸)^5.404 + 10

A = (14⁵)^8.404 + 10

A = 537824³²³² + 10

537824 \(\equiv\) 1 (mod 11)

537824³²³² \(\equiv\) 1³²³² (mod 11) \(\equiv\) 1 (mod 11)

10 \(\equiv\) 10 (mod 11)

⇒ 537824³²³² + 10  \(\equiv\) 1 + 10 (mod 11)

⇒537824³²³² + 10 \(\equiv\) 11 (mod 11) \(\equiv\) 0 (mod 11)

⇒ A = (14⁸)²⁰²⁰ + 10 \(⋮\) 11 (đpcm)

\(14\equiv3\left(mod11\right)\Rightarrow\left(14^8\right)^{2020}\equiv\left(3^8\right)^{2020}\left(mod11\right)\)

\(\left(3^8\right)^{2020}=3^{8.404.5}=\left(3^5\right)^{3232}=\left(243\right)^{3232}\)

\(243\equiv1\left(mod11\right)\Rightarrow243^{3232}\equiv1\left(mod11\right)\)

\(\Rightarrow\left(14^8\right)^{2020}\equiv1\left(mod11\right)\)

\(\Rightarrow\left(14^8\right)^{2020}+10⋮11\)

\(\Rightarrow\) When did he last write to you?

When did he last write to you?

g) (3x + 4)(3x - 4) - (2x + 5)² = (x - 5)² + (2x + 1)² - (x² - 2x) + (x - 1)²

9x² - 16 - 4x² - 20x - 25 = x² - 10x + 25 + 4x² + 4x + 1 - x² + 2x + x² - 2x + 1

5x² - 20x - 41 = 5x² - 6x + 27

5x² - 5x² - 20x + 6x = 27 + 41

-14x = 68

i) -5(x + 3)² + (x - 1)(x + 1) + (2x - 3)² = (5x - 2)² - 5x(5x + 3)

-5(x² + 6x + 9) + x² - 1 + 4x² - 12x + 9 = 25x² - 20x + 4 - 25x² - 15x

-5x² - 30x - 45 + x² - 1 + 4x² - 12x + 9 = -35x + 4

-42x - 37 = -35x + 4

-42x + 35x = 4 + 37

-7x = 41

a) (-x + 5)(x - 2) + (x - 7)(x + 7) = (3x + 1)² - (3x - 2)(3x + 2)

-x² + 2x + 5x - 10 + x² - 49 = 9x² + 6x + 1 - 9x² + 4

7x - 59 = 6x + 5

7x - 6x = 5 + 59

x = 64

b) (5x - 1)(x + 1) - 2(x - 3)² = (x + 2)(3x - 1) - (x + 4)² + (x² - x)

5x² + 5x - x - 1 - 2(x² - 6x + 9) = 3x² - x + 6x - 2 - x² - 8x - 16 + x² - x

5x² + 4x - 1 - 2x² + 12x - 18 = 3x² - 4x - 18

3x² + 16x - 19 = 3x² - 4x - 18

3x² + 16x - 3x² + 4x = -18 + 19

20x = 1

Phân tích nhân tử à bạn?

1

\(n_{Zn}=\dfrac{13}{65}=0,2\left(mol\right)\)

\(n_{Fe_2O_3}=\dfrac{16}{160}=0,1\left(mol\right)\)

a.

\(Zn+2HCl\rightarrow ZnCl_2+H_2\)

0,2------------------------>0,2

\(3H_2+Fe_2O_3\underrightarrow{t^o}2Fe+3H_2O\)

0,2------------>  \(\dfrac{2}{15}\)

b) \(V_{H_2\left(đkc\right)}=0,2.24,79=4,958\left(l\right)\)

c) 

Lập tỉ lệ: \(\dfrac{0,2}{3}>\dfrac{0,1}{1}\Rightarrow Fe_2O_3dư\)

\(m_{Fe}=\dfrac{2}{15}.56=7,47\left(g\right)\)