Rút gọn

a)\(\sqrt{75}+\sqrt{75}-\)\(\sqrt{192}\)

b)3\(\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}+9-6\sqrt{2x}\left(x>0\right)\)

c)3\(\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)

d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)

e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}\sqrt{54}\)

f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)

Giải giúp mình nha

1/ Thực hiện phép tính

a) \(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)

b) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)

2/Rút gọn biểu thức

a) \(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2-1}{x-3}\left(x< 3\right)\)

b) \(4x-\sqrt{8}+\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\left(x>-2\right)\)

3/ Phân tích thành nhân tử

a) \(\sqrt{x}+\sqrt{y}-5\sqrt{xy}-5y\left(x,y\ge0\right)\)

b) \(x\sqrt{x}-y\sqrt{y}\left(x,y\ge0\right)\)

Rút gọn

a) \(\sqrt{75}+\sqrt{48}-\)\(\sqrt{192}\)

b)\(3\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}=9-6\sqrt{2x}\left(x>0\right)\)

c)\(3\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)

d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)

e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}-\sqrt{54}\)

f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
 

1.Cho a,b,c là 3 số dương. Chứng minh :

a) \(\frac{a+1}{b+2c+3}+\frac{b+1}{c+2a+3}+\frac{c+1}{a+2b+3}\ge1\)

b) \(\sqrt{\frac{a}{7a^2+4}}+\sqrt{\frac{a}{7b^2+4}}+\sqrt{\frac{a}{7c^2+4}}\le27\left(\frac{1}{42a+29}+\frac{1}{42b+29}+\frac{1}{42c+29}\right)\)

c) \(c^2-a^2-b^2\le4\left(ĐK:2\le c\le3;\frac{b}{2}+\frac{3}{c}\ge2;a+\frac{b}{2}+\frac{c}{3}\ge3\right)\)

2. Chứng minh :

a) \(2x+\sqrt{12-2x^2}\le6\left(ĐK:6-x^2\ge0\right)\)

b) \(\sqrt{1-2y-y^2}\le y+3\left(ĐK:1-2y-y^2\ge0\right)\)
c) \(\sqrt{5-x^2}+\sqrt{5-\frac{1}{x^2}}+x+\frac{1}{x}\ge6\left(ĐK:5-x^2\ge0;5-\frac{1}{x^2}\ge0\right)\)

Bài 1:Rút gọn

\(a,\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)

\(b,\frac{2}{5-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)

\(c,\left(1+\frac{a+\sqrt{a}}{1+\sqrt{a}}\right)\times\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)+a\left(a\ne1;a\ge0\right)\)

Bài 2: Rút gọn biểu thức

\(P=\frac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)

Rút gọn

\(\dfrac{6}{\sqrt{5}+1}+\sqrt{\dfrac{2}{3-\sqrt{5}}}-\dfrac{10}{\sqrt{5}}\)

B1. Với \(x\ge0,x\ne4.Chobiểuthức\)

\(A=\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}-\dfrac{1}{2-\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\)

\(B=\dfrac{1}{x\sqrt{x}+27}\)

a, tính giá trị biểu thức khi B= 1/4

b, Rút gọn A

c, Tìm giá trị của x để A>1/2

d, Với C= B : A. Tìm GTLN C

1. \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+3-4\sqrt{x-1}}\left(2< x< 5\right)\)

2. \(\frac{6}{1-\sqrt{3}}-\frac{3\sqrt{3}-1}{\sqrt{3}+1}+\sqrt{3}\)

3. \(\sqrt{29-12\sqrt{5}+\sqrt{24-8\sqrt{3}}}\)

4. \(\sqrt{\frac{4}{9-4\sqrt{5}}}-\sqrt{\frac{4}{9+4\sqrt{5}}}\)

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

6. \(\frac{6-\sqrt{6}}{\sqrt{6}-1}-9\sqrt{\frac{2}{3}}-\frac{4}{2-\sqrt{6}}\)

7. \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\frac{\left(\sqrt{x}-1\right)^2}{2}\left(x\ge0,x\ne1\right)\)

Rút gọn biểu thức:

a) \(A=\left(\frac{3x-3\sqrt{x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+2}\right):\frac{1}{\sqrt{x}+2}\left(x\ge0,x\ne1\right)\)

b) \(B=\frac{x\sqrt{x}-3}{x-2\sqrt{x}-3}-\frac{2\left(\sqrt{x-3}\right)}{\sqrt{x}+1}+\frac{\sqrt{x}+3}{3-\sqrt{x}}\left(x>0,x\ne9\right)\)

c) \(C=\frac{2\sqrt{x}-9}{x-5+6}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\left(x\ge0,x\ne4,x\ne9\right)\)