\(=\dfrac{4\left(3-\sqrt{5}\right)}{9-5}-\dfrac{8\left(1-\sqrt{5}\right)}{1-5}+3\sqrt{5}\\ =3-\sqrt{5}-2\left(1-\sqrt{5}\right)+3\sqrt{5}\\ =3+2\sqrt{5}-2+2\sqrt{5}\\ =1-4\sqrt{5}\)
Thực hiến phép tính :
a, \(\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}\)
b, \(\dfrac{2}{3\sqrt{2}-4}-\dfrac{2}{3\sqrt{2}+4}\)
c, \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
d, \(\dfrac{3}{2\sqrt{2}-3\sqrt{3}}-\dfrac{3}{2\sqrt{2}+3\sqrt{3}}\)
e, \(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
g, \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)
Bài 1 :tính giá trị của biểu thức
a) \(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)
b) \(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
c) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4+2\sqrt{3}}\)
d) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
e)\(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
Bài 2 :Tính:
a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)
b) \(\left(2\sqrt{3}+4\right)\left(\sqrt{3}-2\right)\)
c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)
d)\(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
e)\(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
f) \(\dfrac{1}{5}\sqrt{50}-2\sqrt{96}-\dfrac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\dfrac{1}{6}}\)
RÚt gọn c)\(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{899}+\sqrt{900}}\)
d)\(\dfrac{4}{\sqrt{7}-\sqrt{3}}+\dfrac{6}{3+\sqrt{3}}+\dfrac{\sqrt{7}-7}{\sqrt{7}-1}\)
e) \(\dfrac{x+5-x\sqrt{x-1}}{x-1-3\sqrt{x-1}}\)
b) \(\dfrac{\sqrt{5}-\sqrt{15}}{1-\sqrt{3}}-\sqrt{21+4\sqrt{5}}\)
=)) giúp câu nào được thì giúp ạ <3
Giải phương trình
\(a.\dfrac{3}{4}\sqrt{4x}-\sqrt{4x}+5=\dfrac{1}{4}\sqrt{4x}\)
\(b.\sqrt{3-x}-\sqrt{27-9x}+1,25.\sqrt{48-16x}=6\)
\(c.\dfrac{5\sqrt{x}-2}{8\sqrt{x}+2,5}=\dfrac{2}{7}\)
\(d.\sqrt{9x^2+12x+4}=4\)
Giải PT:
a) -5x+7\(\sqrt{x}\) +12=0
b) \(\dfrac{1}{3}\)\(\sqrt{4x^2-20}\) +2\(\sqrt{\dfrac{x^2-5}{9}}\) -3\(\sqrt{x^2-5}=0\)
c) \(\sqrt{9x+27}+5\sqrt{x+3}-\dfrac{3}{4}\sqrt{16x+48}=5\)
d) \(\sqrt{49x-98}-14\sqrt{\dfrac{x-2}{49}}=3\sqrt{x-2}+8\)
Rút gọn
A=\(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)
B=\(\dfrac{5}{4+\sqrt{11}}+\dfrac{11-3\sqrt{11}}{\sqrt{11}-3}-\dfrac{4}{\sqrt{5}-1}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
C=\(\dfrac{\sqrt{x}+1}{x\sqrt[]{x}+x+\sqrt{x}}:\dfrac{1}{x^2-\sqrt{x}}\) (với x>0; x#1)
D=\(\dfrac{\sqrt{x^2-10x+25}}{x-5}\)
Bài 1 :
a) giải phương trình : \(\sqrt{x-3}+\sqrt{y-5}+\sqrt{z-4}=20-\dfrac{4}{\sqrt{x-3}}-\dfrac{9}{\sqrt{y-5}}-\dfrac{25}{\sqrt{z-4}}\)
b) tìm GTLN, GTNN của biểu thức Q=\(\dfrac{-15}{3+\sqrt{6x-x^2-5}}\)
1) Giải phương trình:
\(\sqrt{x-3}+\sqrt{y-5}+\sqrt{z-4}=20-\dfrac{4}{\sqrt{x-3}}-\dfrac{9}{\sqrt{y-5}}-\dfrac{25}{\sqrt{z-4}}\)
2) Tìm GTLN, GTNN của biểu thức:
Q=\(\dfrac{-15}{3+\sqrt{6x-x^2-5}}\)
Rút gọn các biểu thức sau :
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
b) \(0,2\sqrt{\left(-10\right)^2.3}+2\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}\)
c) \(\left(\dfrac{1}{2}\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}\)
d) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2.\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\)
Bài 1 : Thực hiện phép tính , rút gọn biểu thức
A = (\(\sqrt{5}\)-2)(\(\sqrt{5}\)+2)
B = (\(\sqrt{5}\) +\(\sqrt{3}\))(5-\(\sqrt{15}\))
C = (\(\sqrt{45}+\sqrt{63}\))(\(\sqrt{7}-\sqrt{5}\))
D = \(\dfrac{1}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-1}\)
E = \(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
F = \(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\)
G = \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\)
H = \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
I = \(\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)
K = \(\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)
