Tính B = \(\frac{1+xy}{x+y}-\frac{1-xy}{x-y}vớix=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2+\sqrt{2}}}}y=\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
Cho E= \(\dfrac{1+xy}{x+y} - \dfrac{1-xy}{x-y} \)
Biết x= \(\sqrt{4+\sqrt{8}} . \sqrt{2+\sqrt{2 + \sqrt{2}}} . \sqrt{2 -\sqrt{2 +\sqrt{2}}}\)
y =\(\dfrac{ 3 \sqrt{8} -2 \sqrt{12}+ \sqrt{20}}{ 3\sqrt{18} -2\sqrt{27} + \sqrt{45}}\)
Lời giải:
\(x=\sqrt{4+\sqrt{8}}.\sqrt{(2+\sqrt{2+\sqrt{2}})(2-\sqrt{2+\sqrt{2}})}\)
\(=\sqrt{4+2\sqrt{2}}.\sqrt{2^2-(2+\sqrt{2})}=\sqrt{2(2+\sqrt{2})}.\sqrt{2-\sqrt{2}}\)
\(=\sqrt{2}.\sqrt{(2+\sqrt{2})(2-\sqrt{2})}=\sqrt{2}.\sqrt{2^2-2}=2\)
\(y=\frac{6\sqrt{2}-4\sqrt{3}+2\sqrt{5}}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}=\frac{\frac{2}{3}(9\sqrt{2}-6\sqrt{3}+3\sqrt{5})}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}=\frac{2}{3}\)
Do đó:
\(E=\frac{1+xy}{x+y}-\frac{1-xy}{x-y}=\frac{1+\frac{4}{3}}{2+\frac{2}{3}}-\frac{1-\frac{4}{3}}{2-\frac{2}{3}}=\frac{9}{8}\)
Tính \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}-\sqrt{2}}\)
Bài 2:Cho biểu thức \(A=\left(\sqrt{x}+\frac{y-\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\right):\frac{x\sqrt{xy}+y\sqrt{xy}}{\sqrt{xy}\left(y-x\right)}\)
a) Tìm điều kiện của x,y để A có nghĩa
b) Rút gọn A
c) Tính giá trị của A khi \(x=4+2\sqrt{3},y=4-2\sqrt{3}\)
( giải chi tiết hộ mình vs thank iu )
Bài 2 :
a) \(ĐKXĐ:\hept{\begin{cases}x;y>0\\x\ne y\end{cases}}\)
b) \(A=\left(\sqrt{x}+\frac{y-\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\right):\frac{x\sqrt{xy}+y\sqrt{xy}}{\sqrt{xy}\left(y-x\right)}\)
\(\Leftrightarrow A=\frac{x-\sqrt{xy}+y-\sqrt{xy}}{\sqrt{x}-\sqrt{y}}:\frac{x+y}{y-x}\)
\(\Leftrightarrow A=\frac{\left(\sqrt{x}-\sqrt{y}\right)^2}{\sqrt{x}-\sqrt{y}}\cdot\frac{y-x}{x+y}\)
\(\Leftrightarrow A=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(y-x\right)}{x+y}\)
c) Thay \(x=4+2\sqrt{3},y=4-2\sqrt{3}\)vào A, ta được :
\(A=\frac{\left(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\right)\left(4-2\sqrt{3}-4-2\sqrt{3}\right)}{4+2\sqrt{3}+4-2\sqrt{3}}\)
\(\Leftrightarrow A=\frac{\left(\sqrt{\left(1+\sqrt{3}\right)^2}-\sqrt{\left(1-\sqrt{3}\right)^2}\right).\left(-4\sqrt{3}\right)}{8}\)
\(\Leftrightarrow A=\frac{\left(1+\sqrt{3}-\sqrt{3}+1\right).\left(-4\sqrt{3}\right)}{8}=\frac{-8\sqrt{3}}{8}=-\sqrt{3}\)
Vậy ....
Bài 1:
\(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}-\sqrt{2}}=\frac{2\sqrt{2\cdot4}-\sqrt{3\cdot4}}{\sqrt{2\cdot9}-\sqrt{16\cdot3}}-\frac{\sqrt{5}+\sqrt{9\cdot3}}{\sqrt{30}-\sqrt{2}}\)
\(=\frac{4\sqrt{2}-2\sqrt{3}}{3\sqrt{2}-4\sqrt{3}}-\frac{\sqrt{5}+3\sqrt{3}}{\sqrt{30}-\sqrt{2}}=\frac{\left(4\sqrt{2}-2\sqrt{3}\right)\left(\sqrt{30}-\sqrt{2}\right)-\left(\sqrt{5}+3\sqrt{3}\right)\left(3\sqrt{2}-4\sqrt{3}\right)}{\left(3\sqrt{2}-4\sqrt{3}\right)\left(\sqrt{30}-\sqrt{2}\right)}\)
\(=\frac{4\sqrt{60}-8-2\sqrt{90}+2\sqrt{6}-3\sqrt{10}+4\sqrt{15}-9\sqrt{6}+36}{3\sqrt{60}-6-4\sqrt{90}+4\sqrt{6}}\)
\(=\frac{8\sqrt{15}-8-6\sqrt{10}+2\sqrt{6}-3\sqrt{10}+4\sqrt{15}-9\sqrt{6}+36}{6\sqrt{15}-6-12\sqrt{10}+4\sqrt{6}}\)
\(=\frac{12\sqrt{15}-2\sqrt{10}-7\sqrt{6}+28}{6\sqrt{15}-12\sqrt{10}+4\sqrt{6}-6}\)
Cho E=\(\dfrac{1+xy}{x+y}-\dfrac{1-xy}{x-y}\)Tính giá trị của E biết:
x=\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
y=\(\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
cho \(x=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2-\sqrt{2}}}\)
\(y=\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
Tính giá trị biểu thức:\(Q=\dfrac{xy+1}{x+y}+\dfrac{1-xy}{x-y}\)
\(A=\left(\sqrt{5}-\sqrt{2}\right)^2-\frac{9}{\sqrt{10}-1}+\sqrt{90}\)\(B=\sqrt{2}\left(3\sqrt{2}+\sqrt{3-\sqrt{5}}\right)-\sqrt{5}\)\(C=\left(\frac{5-\sqrt{5}}{\sqrt{5}-1}-\frac{\sqrt{5}+1}{5+\sqrt{5}}\right):\frac{\sqrt{5}+1}{\sqrt{5}}\)\(D=\frac{x\sqrt{y}-y\sqrt{x}+\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}:\frac{x+2\sqrt{xy}+y}{\left(\sqrt{x}+\sqrt{y}\right)^3\left(x+y\right)}vớix,y>0\)
TÍNH HOẶC RÚT GỌN
1. Tính:
a) A= \(\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)(dấu căn đầu tiên là của cả biểu thức)
b) B= \(\frac{2}{\sqrt{3}}+\frac{\sqrt{2}}{3}+\frac{2}{\sqrt{3}}.\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}\)
2. Cho:
A= \(\left(\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right).\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{x}+\frac{1}{y}\right):\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{x^3y}+\sqrt{xy^3}}\)với x>0, y>0
a) Rút gọn A
b) Cho xy=16. Tìm x,y để A có GTNN. Tìm Gt đó
Bạn chỉ mình cách viết phân số đi, mình làm ra luôn cho.
vào chữ fx rồi chọn biểu tượng phân số là xong
Rút gọn biểu thức
a)\(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
b)\(\sqrt{11-4\sqrt{7}}-\sqrt{2}\cdot\sqrt{8+3\sqrt{7}}\)
c)\(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}\)
d)\(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}\left(x>0;x\ne1\right)\)
e)\(\frac{4-4\sqrt{x}}{x-2\sqrt{x}-35}+\frac{2}{\sqrt{x}-7}-\frac{3}{\sqrt{x}+5}\left(x\ge0:x\ne49\right)\)
f)\(\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}\)
f)\(\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}\)
\(=\frac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{xy}}.\left(\sqrt{x}-\sqrt{y}\right)\)
\(=x-y\)
b)\(\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
\(=\sqrt{7-4\sqrt{7}+4}-\sqrt{16+6\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\sqrt{9+6\sqrt{7}+7}\)
\(=\sqrt{7}-2-\sqrt{\left(3+\sqrt{7}\right)^2}\)(vì \(\sqrt{7}>2\))
\(=\sqrt{7}-2-3-\sqrt{7}=-5\)
c)\(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}=\frac{\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}=\frac{\sqrt{x}}{\sqrt{y}}=\frac{\sqrt{xy}}{y}\)
d)\(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}=\frac{x-2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}-1}{\sqrt{x}}=\frac{x-\sqrt{x}}{x}\)
35Cho biểu thức
P=\(\left[\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{x}+\frac{1}{y}\right]:\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{xy^3}+\sqrt{x^3y}}\)
a) Rút gọn P
b)Cho xy=16 . Tìm Min P
34 Cho biểu thức
P=\(\frac{x}{\sqrt{xy}-2y}-\frac{2\sqrt{x}}{x+\sqrt{x}-2\sqrt{xy}-2\sqrt{y}}-\frac{1-x}{1-\sqrt{x}}\)
a) Rút gọn P
b)Tính P biết 2x^2+y^2-4x-2xy+4=0
bài 1) rút gọn
1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)
bài 2) với các biểu thức đã cho là có nghĩa và rút gọn
1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)