\(4\sqrt{8}-2\sqrt{50}+\dfrac{5}{6}\sqrt{72}\)

\(=4.2\sqrt{2}-2.5\sqrt{2}+\dfrac{5}{6}.6\sqrt{2}\)

\(=8\sqrt{2}-10\sqrt{2}+5\sqrt{2}\)

\(=3\sqrt{2}\)

*) \(y\times2\dfrac{3}{5}+1=3\dfrac{9}{10}\)

\(y\times\dfrac{13}{5}+1=\dfrac{39}{10}\)

\(y\times\dfrac{13}{5}=\dfrac{39}{10}-1\)

\(y\times\dfrac{13}{5}=\dfrac{29}{10}\)

\(y=\dfrac{29}{10}:\dfrac{13}{5}\)

\(y=\dfrac{87}{50}\)

*) \(y:4\dfrac{1}{4}-3=3\dfrac{1}{5}\)

\(y:\dfrac{17}{4}-3=\dfrac{16}{5}\)

\(y:\dfrac{17}{4}=\dfrac{16}{5}+3\)

\(y:\dfrac{17}{4}=\dfrac{31}{5}\)

\(y=\dfrac{31}{5}\times\dfrac{17}{4}\)

\(y=\dfrac{527}{20}\)

ĐKXĐ: \(x\ne-3;x\ne3\)

\(\dfrac{2\sqrt{x}}{\sqrt{x}+3}-\dfrac{\sqrt{x}+1}{3-\sqrt{x}}-\dfrac{3-11\sqrt{x}}{x-9}\)

\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}-\dfrac{3-11\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{3-11\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}+\sqrt{x}+3-3+11\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{3x+9\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{3\sqrt{x}}{\sqrt{x}-3}\)

\(3^{39}=\left(3^{13}\right)^3=1594323^3\)

\(11^{21}=\left(11^7\right)^3=19487171^3\)

Do 1594323 < 19487171 nên \(1594323^3< 19487171^3\)

Vậy \(3^{39}< 11^{21}\)

\(3^{39}=\left(3^{13}\right)^3=1594323^3\)

\(11^{21}=\left(11^7\right)^3=19487171^3\)

Do 1594323 < 19487171 nên \(1594323^3< 19487171^3\)

Vậy \(3^{39}< 11^{21}\)

Hiệu hai số đó là: 14 × 2 = 28

Số lớn là: (848 + 28) : 2 = 438

Số bé là: (848 - 28) : 2 = 410

8) (a + b/2)³

= a³ + 3.a².b/2 + 3.a.(b/2)² + (b/2)³

= a³ + 3/2 a²b + 3/4 ab² + b³/8

9) Viết sai đề

10) (3x + 1/2)³

= (3x)³ + 3.(3x)².1/2 + 3.3x.(1/2)² + (1/2)³

= 27x³ + 27/2 x² + 9/4 x + 1/8

11) Viết sai đề

Ta có: 3A = 3² + 3³ + 3⁴ + ... + 3²⁰⁰¹

Suy ra 2A = 3A - A = (3² + 3³ + 3⁴ + ... + 3²⁰⁰¹) - (3 + 3² + 3³ + ... + 3²⁰⁰⁰)

= 3²⁰⁰¹ - 3

Suy ra 2A + 3 = 3²⁰⁰¹ - 3 + 3 = 3²⁰⁰¹

Mà 2A + 3 = 3^n

Suy ra 3^n = 3²⁰⁰¹

Suy ra n = 2001