Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Bài 1: Tính
1, Aleft(1-frac{5+sqrt{5}}{1+sqrt{5}}right).left(frac{5-sqrt{5}}{1-sqrt{5}}-1right)
2, Bleft(frac{3sqrt{125}}{15}-frac{10-4sqrt{6}}{sqrt{5}-2}right).frac{1}{sqrt{5}}
3, Cleft(frac{sqrt{1000}}{100}-frac{5sqrt{2}-2sqrt{5}}{2sqrt{5}-8}right).frac{sqrt{10}}{10}
4, Dfrac{1}{sqrt{49+20sqrt{6}}}-frac{1}{sqrt{49-20sqrt{6}}}+frac{1}{sqrt{7-4sqrt{3}}}
5, Efrac{1}{sqrt{4-2sqrt{3}}}-frac{1}{sqrt{7-sqrt{48}}}+frac{3}{sqrt{14-6sqrt{5}}}
6, Ffrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}...
Đọc tiếp
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
tính: \(x=\sqrt{1+999^2+\dfrac{999^2}{1000^2}}+\dfrac{999}{1000}\)
Tính
P= \(\sqrt{1+999^2+\dfrac{999^2}{1000^2}}\)+\(\dfrac{999}{1000}\)
X1000 + Y1000 = 6,912
X2000 + Y2000 = 33,76244
X3000 + Y3000 = ?
cho ba số x,y,z thỏa mãn đồng thời :\(\left\{{}\begin{matrix}x-2\sqrt{y}+1=0\\y-2\sqrt{z}+1=0\\z-2\sqrt{x}+1=0\end{matrix}\right.\)
tính giá trị của biểu thức A= x1000 +y1000+z1000
Giải hệ phương trình:
\(\hept{\begin{cases}\frac{1}{x}+\frac{1}{y+z}=\frac{1}{2}\\\frac{1}{y}+\frac{1}{x+z}=\frac{1}{3}\\\frac{1}{z}+\frac{1}{x+y}=\frac{1}{4}\end{cases}}\)
Rút gọn
\(\frac{1}{(a+b)^3}(\frac{1}{a^3}+\frac{1}{b^3})+\frac{3}{(a+b)^4}(\frac{1}{a^2}+\frac{1}{b^2})+ \frac{6}{(a+b)^5}(\frac{1}{a}+\frac{1}{b})\)
Rút gọn: \(A=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+\sqrt{1+\frac{1}{4^2}+\frac{1}{5^2}}+...+\sqrt{1+\frac{1}{k^2}+\frac{1}{\left(k+1\right)^2}}\)
tính:
\(\frac{\frac{1}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{\frac{1}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}\)