\(H^3=9+4\sqrt{5}+9-4\sqrt{5}+3\sqrt[3]{\left(9+4\sqrt{5}\right)\left(9-4\sqrt{5}\right)}H\)
\(H^3=18+3H\)
\(H^3-3H-18=0\)
\(H=3\)
Rut gon P = \(\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
1) a) Rut gon \(A=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\left(x\ge0\right),x\ne4\)
Rut gon P=\(\dfrac{\sqrt{a+1}+1}{\sqrt{a+1}-2}+\dfrac{2+5\sqrt{a+1}}{3-a}+\dfrac{2\sqrt{a+1}}{\sqrt{a+1}+2}\) (voi a#3, a>0)
Cho P = \(\dfrac{x^2+5\sqrt{x^2+1}+7}{\sqrt{x^2+1}+3}\) + \(\dfrac{x^2+7\sqrt{x^2+1}+13}{\sqrt{x^2+1}+4}\)
a/ Rut gon P
b/ Tim x de P = 11
Rút gọn các biểu thức :
\(a,\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
b, \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
rut gon
\(\left(\sqrt{5-2\sqrt{2\sqrt{2}-2}}+\sqrt{2}-1\right)\sqrt{\sqrt{2}-1}\)
Thực hiện phép tính:
a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)
e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)
h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
Cho A = \(\frac{3\sqrt{x}-3}{x\sqrt{x}-2x+2\sqrt{x}-1}-\frac{4x\sqrt{x}-4}{x^3-1}\)(x>1). Rut gon A va tim x de A=1
Rút gọn
H=\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
F=\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
G=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
E=\(\frac{2\sqrt{3+\sqrt{5-13+\sqrt{48}}}}{\sqrt{6}+\sqrt{2}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Z=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)