a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

 a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

a) 32 - 6 . (8 - 2³) + 18 =  32 - 6 . (8 - 8) + 18

= 32 - 6 . 0 + 18 = 32 + 18 = 50

b) (3 . 5 - 9)³ . (1 + 2 . 3)² + 4²

= (15 - 9)³ . (1 + 6)² + 4²

= 6³ . 7² + 4² = 216 . 49 + 16 = 10 584 + 16 = 10 600

a) 32 - 6 . (8 - 2³) + 18 =  32 - 6 . (8 - 8) + 18

= 32 - 6 . 0 + 18 = 32 + 18 = 50

b) (3 . 5 - 9)³ . (1 + 2 . 3)² + 4²

= (15 - 9)³ . (1 + 6)² + 4²

= 6³ . 7² + 4² = 216 . 49 + 16 = 10 584 + 16 = 10 600

`A=sqrt{8+2sqrt7}-sqrt{8-2sqrt7}`

`=sqrt{7+2sqrt7+1}-sqrt{7-2sqrt7+1}`

`=sqrt{(sqrt7+1)^2}-sqrt{(sqrt7-1)^2}`

`=sqrt7+1-sqrt7+1=2`

`B=sqrt{11-6sqrt2}+sqrt{6-4sqrt2}`

`=sqrt{9-2.3.sqrt2+2}+sqrt{4-2.2.sqrt2+2}`

`=sqrt{(3-sqrt2)^2}+sqrt{(2-sqrt2)^2}`

`=3-sqrt2+2-sqrt2=5-2sqrt2`

a: \(2\dfrac{3}{5}+1\dfrac{2}{5}\cdot\dfrac{31}{2}\)

\(=\dfrac{13}{5}+\dfrac{7}{5}\cdot\dfrac{31}{2}\)

\(=\dfrac{26}{10}+\dfrac{217}{10}=\dfrac{243}{10}\)

b: \(4\dfrac{3}{4}-3\dfrac{2}{3}:1\dfrac{1}{6}\)

\(=\dfrac{19}{4}-\dfrac{11}{3}:\dfrac{7}{6}\)

\(=\dfrac{19}{4}-\dfrac{11}{3}\cdot\dfrac{6}{7}\)

\(=\dfrac{19}{4}-\dfrac{22}{7}\)

\(=\dfrac{19\cdot7-22\cdot4}{28}=\dfrac{45}{28}\)

a) Có x = 2020 => x + 1 = 2021. Thay 2021 = x + 1 vào A

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

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

\(A=1\)

b) Có x = -19 => x - 1 = -20 => - ( x - 1 ) = 20. Thay 20 = - ( x - 1) vào B

\(B=x^{10}-\left(x-1\right)x^9-\left(x-1\right)x^8-\left(x-1\right)x^7-...-\left(x-1\right)x^2-\left(x-1\right)x-x+1\)

\(B=x^{10}-x^{10}+x^9-x^9+...+x^2-x^2+x-x+1\)

\(B=1\)

Chúc bạn học tốt!!!

16/5

17/4

a. 7/2 - 3/10 = 16/5

b. (4/6 + 5):4/3=17/3 :4/3=17/4

a) \(6-\dfrac{5}{2}-\dfrac{3}{10}=\dfrac{7}{2}-\dfrac{3}{10}=\dfrac{16}{5}\)

b) \(\dfrac{4}{6}\div\dfrac{4}{3}+5\div\dfrac{4}{3}\)

    \(=\dfrac{1}{2}+\dfrac{15}{4}\)

     \(=\dfrac{17}{4}\)

\(A=\left(4+\sqrt{3}\right)\sqrt{19-8\sqrt{3}}\)

\(A=\left(4+\sqrt{3}\right)\sqrt{4^2-2\cdot4\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\)

\(A=\left(4+\sqrt{3}\right)\sqrt{\left(4-\sqrt{3}\right)^2}\)

\(A=\left(4+\sqrt{3}\right)\left(4-\sqrt{3}\right)\)

\(A=4^2-3\)

\(A=13\)

\(B=\dfrac{3}{4+\sqrt{13}}+\dfrac{\sqrt{52}}{2}-3\)

\(B=\dfrac{3\left(4-\sqrt{13}\right)}{\left(4-\sqrt{13}\right)\left(4+\sqrt{13}\right)}+\dfrac{2\sqrt{13}}{2}-3\)

\(B=\dfrac{3\left(4-\sqrt{13}\right)}{16-13}+\sqrt{13}-3\)

\(B=4-\sqrt{13}+\sqrt{13}-3\)

\(B=4-3\)

\(B=1\)

21/10

17/4

a) 6/1x 2/5-3/10

= 12/5- 3/10

= 21/10

b) (4/6+5):4/3

= 17/3x 3/4

= 17/4

a) 6 : 5/2 - 3/10 = 12/5 - 3/10 = 21/10

b) 4/6 : 4/3 + 5 : 4/3 = 1/2 + 5 : 4/3 = 1/2 + 15 /4 = 17/4

a)

`6:5/2-3/10`

`=6xx2/5-3/10`

`=12/5-3/10`

`=24/10-3/10`

`=21/10`

b)

`4/6:4/3+5:4/3`

`=2/3xx3/4+5xx3/4`

`=3/4xx(2/3+5)`

`=3/4xx(2/3+15/3)`

`=3/4xx17/3`

`=17/4`

\(a,6:\dfrac{5}{2}-\dfrac{3}{10}\\ =\dfrac{6}{1}:\dfrac{5}{2}-\dfrac{3}{10}\\ =\dfrac{6}{1}\times\dfrac{5}{2}-\dfrac{3}{10}\\ =\dfrac{12}{5}-\dfrac{3}{10}\\ =\dfrac{12\times2}{5\times2}-\dfrac{3}{10}\\ =\dfrac{24}{10}-\dfrac{3}{10}\\ =\dfrac{21}{10}\) 

\(b,\dfrac{4}{6}:\dfrac{4}{3}+5:\dfrac{4}{3}\\ =\dfrac{4}{6}:\dfrac{4}{3}+\dfrac{5}{1}:\dfrac{4}{3}\\ =\dfrac{4}{3}:\left(\dfrac{4}{6}+\dfrac{5}{1}\right)\\ =\dfrac{4}{3}:\left(\dfrac{4}{6}+\dfrac{5\times6}{1\times6}\right)\\ =\dfrac{4}{3}:\left(\dfrac{4}{6}+\dfrac{30}{6}\right)\\ =\dfrac{4}{3}:\dfrac{34}{6}\\ =\dfrac{4}{3}:\dfrac{17}{3}\\ =\dfrac{4}{3}\times\dfrac{3}{17}\\=\dfrac{12}{51} \\ =\dfrac{4}{17}.\)

\(a,6:\dfrac{5}{2}-\dfrac{3}{10}=6\times\dfrac{5}{2}-\dfrac{3}{10}=\dfrac{12}{5}-\dfrac{3}{10}=\dfrac{24}{10}-\dfrac{3}{10}=\dfrac{21}{10}\)

\(b,\dfrac{4}{6}:\dfrac{4}{3}+5:\dfrac{4}{3}=\dfrac{4}{6}\times\dfrac{3}{4}+5\times\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{15}{4}=\dfrac{17}{4}\)