a) Ta có: \(VT=\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)
\(=\sqrt{\left(9-\sqrt{17}\right)\cdot\left(9+\sqrt{17}\right)}\)
\(=\sqrt{81-17}=\sqrt{64}=8\)=VP(đpcm)
b) Ta có: \(VT=2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
\(=2\sqrt{6}-4\sqrt{2}+1+4\sqrt{2}+8-2\sqrt{6}\)
=9=VP(đpcm)
1. Thực hiện phép tính
a. \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
b. \(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)
Thực hiện phép tính:
A=\(\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right).\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right).\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right).\left(-\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\)
B=\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{5}}\)
C=\(\left(\sqrt{3}-\sqrt{2}\right).\sqrt{5-2\sqrt{6}}\)
D=\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
C/Minh đẳng thức:
a) \(\left(\frac{\sqrt{a}+2}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right).\frac{\sqrt{a}+1}{\sqrt{a}}=\frac{2}{a-1}\) (với a>0, b>0, a≠b)
b)\(\frac{2}{\sqrt{ab}}:\left(\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{b}}\right)^2-\frac{a+b}{\left(\sqrt{a}-\sqrt{b}\right)^2}=-1\) (với a>0, b>0,a≠b)
c) \(\frac{2\sqrt{a}+3\sqrt{b}}{\sqrt{ab}+2\sqrt{a}-3\sqrt{b}-6}-\frac{6-\sqrt{ab}}{\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6}=\frac{a+9}{a-9}\) (với a≥0, b≥0,a≠9)
Rút gọn
a)\(\sqrt{\left(4+\sqrt{2}\right)^2}\)
b)\(-4\sqrt{\left(-3\right)^6}\)
c)\(\sqrt{\left(4-\sqrt{17}\right)^2}\)
d)\(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(x-2\right)^8}\)
Giải các phương trình sau:
a, \(\sqrt{x^2-6x+9}+\sqrt{2x^2+8x+8}=\sqrt{x^2-2x+1}\)
b, \(\sqrt{x-3-2\sqrt{x-4}}+\sqrt{x-4\sqrt{x-1}}=1\)
c. \(\sqrt{x+8-6\sqrt{x-1}}=4\)
d, \(\sqrt{x\left(x-3\right)}+\sqrt{x\left(x-4\right)}=2\sqrt{x^2}\)
e, \(\sqrt{\left(x+3\right)\left(x+2\right)}+\sqrt{\left(x+3\right)\left(x-1\right)}=2\sqrt{\left(x+3\right)^2}\)
câu 1. đơn giản biểu thức
a. A = \(\sqrt{a^2+6a+9}+\sqrt{a^2-6a+9}\)
b. B = \(\left(\sqrt{3-\sqrt{7}}\right)^6\)
c. C = \(\left(\sqrt{\sqrt{2}-\sqrt{3}}\right)^2\)
d. D = \(\sqrt{3+2\sqrt{2}}\)
e. E = \(\sqrt{8-2\sqrt{15}}\)
Thực hiện phép tính:
a)\(\frac{5}{a-\sqrt{11}}+\frac{1}{3\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
b)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
c)\(\left(\frac{9-2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2-\left(\frac{9+2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2\)
Tính giá trị của biểu thức: \(B=\left(x-y\right)^3+3\left(x-y\right)\left(xy+1\right)+20\sqrt{2}-2332017\) , biết: \(x=\sqrt[3]{3+2\sqrt{2}}-\sqrt[3]{3-2\sqrt{2}},y=\sqrt[3]{17+12\sqrt{2}}-\sqrt[3]{17-12\sqrt{2}}\)
1) Rút gọn biểu thức
P=\(\left(1-\dfrac{x-3\sqrt{x}}{x-9}\right):\left(\dfrac{\sqrt{x}-3}{2-\sqrt{x}}+\dfrac{\sqrt{x}-2}{3+\sqrt{x}}-\dfrac{9-x}{x+\sqrt{x}-6}\right)\)
