\(P=\dfrac{\sqrt[3]{2}+\sqrt{5+2\sqrt{5.2}+2}+\sqrt[3]{1-3\sqrt[3]{2}+3\sqrt[3]{4}-2}}{\sqrt{5}+\sqrt{2}+1}\)
\(P=\dfrac{\sqrt[3]{2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}+\sqrt[3]{\left(1-\sqrt[3]{2}\right)^3}}{\sqrt{5}+\sqrt{2}+1}\)
\(P=\dfrac{\sqrt[3]{2}+\sqrt{5}+\sqrt{2}+1-\sqrt[3]{2}}{\sqrt{5}+\sqrt{2}+1}\)
\(P=\dfrac{\sqrt{5}+\sqrt{2}+1}{\sqrt{5}+\sqrt{2}+1}=1\)
Cho biểu thức P=\(\left(\dfrac{2\sqrt{x}+x}{x\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
a, Rút gọn P.
b,Tính \(\sqrt{P}\) khi x=5 +2\(\sqrt{3}\)
Rút gọn :
a) \(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}+\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
b) \(\sqrt{\left(\sqrt{5}-1\right).\sqrt{13-\sqrt{69-28\sqrt{5}}}}\)
c) \(\dfrac{\sqrt{3+\sqrt{5}}.\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{10}+\sqrt{2}\right)\left(3-\sqrt{5}\right)}{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}\)
Giải phương trình:
1. \(5x^2+2x+10=7\sqrt{x^4+4}\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\sqrt{x^2+2x}=\sqrt{3x^2+4x+1}-\sqrt{3x^2+4x+1}\)
rút gọn
\(\sqrt{3}+\sqrt{11+6\sqrt{ }2}-\sqrt{5}+2\sqrt{6}\)\(\sqrt{2}+\sqrt{6+2\sqrt{ }5}-\sqrt{7+2\sqrt{ }10}\)
\(\sqrt{6+\sqrt{ }6+\sqrt{ }6+\sqrt{ }6........}\)
\(\sqrt{3+\sqrt{ }5+2\sqrt{ }3}+\sqrt{3-\sqrt{ }5+2\sqrt{ }3}\)
\(\sqrt{227-30\sqrt{ }2}+\sqrt{123}+22\sqrt{2}\)
Cho biểu thức : P= 1+\(\left(\dfrac{2a+\sqrt{a}-1}{1-a}-\dfrac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\dfrac{a-\sqrt{a}}{2\sqrt{a}-1}\)
a,Rút gọn P .
b,Chứng minh rằng \(P>\dfrac{2}{3}\)
c,Cho \(P=\dfrac{\sqrt{6}}{1+\sqrt{6}}\) ,tìm giá trị của a?
Thực hiện phép tính:
\(A=\dfrac{\sqrt{5+\sqrt{17}}-\sqrt{5-\sqrt{17}}-\sqrt{10-4\sqrt{2}}+4}{\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}+2-\sqrt{2}}\)
1/Giải phương trình:
a. \(3x+4y=5\sqrt{x^2+y^2}\)
b. \(\dfrac{xy\sqrt{z-5}+xz\sqrt{y-4}+yz\sqrt{x-3}}{xyz}=\dfrac{10\sqrt{3}+15+6\sqrt{5}}{60}\)
c. \(\sqrt{\dfrac{x^2+x+1}{x}}+\sqrt{\dfrac{x}{x^2+x+1}}=\dfrac{2018}{2019}\)
d.\(\sqrt{x+x^2}+\sqrt{x-x^2}=x+1\)
e. \(\dfrac{\sqrt{x-1}}{x}+\dfrac{\sqrt{y-1}}{y}=1\)
2/Giải phương trình:
a.\(\sqrt{x-2}-\sqrt{2x-3}=\dfrac{1-x}{2x-3}\)
b.\(x^2+\dfrac{x^2}{\left(x+1\right)^2}=3\)
Giải các phương trình sau theo phương pháp đặt ẩn phụ:
a.{\(\dfrac{12}{x-3}-\dfrac{5}{y+2}=63\)
\(\dfrac{8}{x-3}+\dfrac{15}{y+2}=-13\)
b.{\(4\sqrt{x+3}-9\sqrt{y+1}=2\)
\(5\sqrt{x+3}+3\sqrt{y+1}=31\)
Rút gọn
a,\(\sqrt{227-30\sqrt{2}}\) + \(\sqrt{123+22\sqrt{2}}\)
b,\(\dfrac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)
c, \(\sqrt{2-\sqrt{3}}\) (\(\sqrt{5}\) + \(\sqrt{2}\))
