bài 1) rút gọn

1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)

bài 2) với các biểu thức đã cho là có nghĩa và rút gọn

1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)

giải các phương trình sau

1) 15.\(\sqrt{x^3-1}\)=4x²+8

2) \(\sqrt{2x-3}\)+6=2x+\(\sqrt{x}\)

3) \(\sqrt{x-\frac{1}{x}}\)+\(\frac{4}{x}\)=x+\(\sqrt{2x-\frac{5}{x}}\)

4)\(\sqrt{5x-1}\)-\(\sqrt{x+2}\)=\(\frac{4x-3}{5}\)

5) \(\sqrt{2x-\frac{3}{x}}\)-1=\(\frac{3}{2x}\)-\(\sqrt{\frac{6}{x}-2x}\)

Giair phương trình sau:

1. (x - 3) (x + 4) = (2 - x) (1 - x)

2. \(\frac{2x}{15}\) - \(\frac{15-2x}{10}\) = \(\frac{7}{6}\)

3. \(\frac{x}{15}\) + \(\frac{x+1}{16}\) + \(\frac{x+2}{17}\) + \(\frac{x+3}{18}\) + \(\frac{x+4}{19}\) = 5

4. \(\frac{x+1}{11}\) + \(\frac{2x-5}{15}\) = \(\frac{3x-47}{17}\) - \(\frac{4x-59}{19}\)

5. x² + 9x + 20 = 0

6. x³ + 2x - 3 = 0

3. a.\(\sqrt{\left(4-\sqrt{17}\right)^2}\)

b.\(\frac{2\sqrt{3}}{2}\)

c \(\frac{\sqrt{6}+\sqrt{14}}{\text{2√3+√28}}\)

d.\(\frac{x+1}{\sqrt{x^2-1}}\)

e.\(\frac{x^2-5}{x+\sqrt{5}}\)

f.\(\frac{2}{2-\sqrt{3}}\)

g.\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)

f.\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)

i.\(\frac{3}{\sqrt{20}}+\frac{1}{\sqrt{60}}-2\sqrt{\frac{1}{15}}\)

k.\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)

i.(\(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\))\(\sqrt{5}\)

h.\(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)

l.\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)

m.\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{\frac{4}{3}}\)

n.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)

d\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)

1, \(\frac{x}{2}-\frac{3-x}{3}=\frac{2x+2}{5}\)

2,1-\(\frac{3-x}{3}=\frac{2x+2}{5}-\frac{2-x}{4}\)

3,\(\frac{2}{3}x+1=x-5\)

4, 2x-x² =0

5,\(\frac{4x}{x+1}+\frac{x+3}{x}=6\)

6, \(\frac{x-1}{x-3}+\frac{2x+2}{x-2}=8\)

7, \(\sqrt{x-1}=\sqrt{2}\)

8, \(\sqrt{2x-1}=\sqrt{x}-4\)

Rút gọn :

a, \(-\sqrt{36b}\) - \(\frac{1}{3}\sqrt{54b}\) + \(\frac{1}{5}\sqrt{150b}\) ( b ≥ 0 )

b, \(5\sqrt{\frac{x}{y}}\) - \(4\sqrt{\frac{y}{x}}\) + \(\frac{1}{xy}\) (x > 0 , y > 0 )

c, \(\frac{1}{\sqrt{x-1}}\) + \(\frac{1}{1+\sqrt{x}}\) + 1 ( x ≥ 0 , x ≠ 1 )

`Cho x>0 thỏa : x\(^2\)+\(\frac{1}{x^2}\)=7 .Hãy tính x\(^5\)+\(\frac{1}{x^5}\).

                        Giải

ta có x\(^2\)+\(\frac{1}{x^2}\)=7

<=>\(\frac{x^4}{x^2}\)=7          <=>\(\sqrt{\frac{x^4}{x^2}}\)=\(\sqrt{7}\)<=> \(\frac{x^2}{x}\)=\(\sqrt{7}\)  <=> x = \(\sqrt{7}\)

Rồi thay x = \(\sqrt{7}\) vào x\(^5\)+\(\frac{1}{x^5}\).

làm theo cách này có đúng hay không ?