Bạn xem lại đề bài 1 và 2.b nhé !
2/ \(A=\sqrt{\left(3-5\sqrt{2}\right)^2}-\sqrt{51+10\sqrt{2}}\)
\(A=5\sqrt{2}-3-\sqrt{\left(5\sqrt{2}+1\right)^2}\)
\(A=5\sqrt{2}-3-5\sqrt{2}-1\)
\(A=-4\)
Bạn xem lại đề bài 1 và 2.b nhé !
2/ \(A=\sqrt{\left(3-5\sqrt{2}\right)^2}-\sqrt{51+10\sqrt{2}}\)
\(A=5\sqrt{2}-3-\sqrt{\left(5\sqrt{2}+1\right)^2}\)
\(A=5\sqrt{2}-3-5\sqrt{2}-1\)
\(A=-4\)
TÌM GIÁ TRỊ LỚN NHẤT (có thể dùng BĐT côsi)
\(y=\left|x\right|\sqrt{25-x^2}Với-5\le x\le5\)
\(f\left(x\right)=\frac{x}{2}+\sqrt{1-x-2x^2}\)
\(E=\frac{\sqrt{x-1}}{x}+\frac{\sqrt{y-2}}{y}+\frac{\sqrt{z-3}}{z}\)
TÍNH
\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+\sqrt{1+\frac{1}{4^2}+\frac{1}{5^2}}+...+\sqrt{1+\frac{1}{2012^2}+\frac{1}{2013^2}}\)
GIÚP EM ĐI Ạ, MAI EM PHẢI KIỂM TRA RỒI
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. \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\frac{\left(\sqrt{x}-1\right)^2}{2}\left(x\ge0,x\ne1\right)\)
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
Bài 1:
a, A=\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
b, B= \(\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right).\frac{1}{\left(\sqrt{2}+1\right)^2}\)
Bài 2: Giải pt
a,\(\frac{5\sqrt{x}-2}{8\sqrt{x}+2,5}=\frac{2}{7}\)
b, \(\sqrt{x^2-6x+9}=\sqrt{4+2\sqrt{3}}\)
Bài 3:
A=\(\left(\frac{x+2}{x\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\right).\frac{4\sqrt{x}}{3}\)
Tính A=\(\left(\frac{2}{\sqrt{5}-3}-\frac{2}{\sqrt{5}+3}\right)×\frac{\sqrt{3}-3}{1-\sqrt{3}}+3\sqrt{27}\)
B=\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)×\left(11+\sqrt{6}\right)\)
Tìm x để E=\(\sqrt{x-5}+\sqrt{7}\)nhỏ nhất
Tìm x để F=\(\frac{4-\sqrt{x}}{\sqrt{x}+2}\)lớn nhất
Bài 1: Rút gọn
a. \(\left(5-2\sqrt{3}\right)^2+\left(5+2\sqrt{3}\right)^2\)
b. \(\left(\sqrt{5}+\sqrt{2}\right)^2-\left(2\sqrt{5}+1\right)\left(2\sqrt{5}-1\right)-\sqrt{40}\)
c. \(\left(\sqrt{2}-1\right)^2-\frac{2}{3}\sqrt{4}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{15}}-\sqrt{2}\)
d. \(\left(\sqrt{6}-\sqrt{18}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right)2\sqrt{6}+2\sqrt{3}\)
e. \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+6\sqrt{6}+3\sqrt{24}\)
Bài 2: Rút gọn
A =\(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}:\frac{\sqrt{x+1}}{x-2\sqrt{x}+1}\right)\)(x>0 ; x khác 1)
giúp vs
1)a) n thuộc N*: rút gọn:
K = \(\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}\)
b) tính
I = \(\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2015^2}+\frac{1}{2016^2}}+\sqrt{1+\frac{1}{2016^2}+\frac{1}{2017^2}}\)2) A= \(\sqrt{x^2-6x+9}-\sqrt{x^2+6x+9}\)
a) rút gọn A
b) tìm x đề A=1
3) rút gọn B = \(\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\)
4) tính: \(\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
C= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
a)\(\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
b) \(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}+4}+\frac{\sqrt{x}-4}{\sqrt{x}+1}+\frac{\sqrt{x}+8}{4-\sqrt{2}}\)
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)