\(\frac{\left(\sqrt{5}+2-8\sqrt{5}\right)}{2\sqrt{5}-4}\)rút gọn bt
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6 tháng 7 2019
A = \(\frac{8}{\sqrt{5}-1}\) - (\(2\sqrt{5}-1\) ) ( chúng ta cần trục căn thức lên để khử mẫu )
= \(\frac{8\left(\sqrt{5}+1\right)}{5-1}\)- \(\left(2\sqrt{5}-1\right)\)
= \(2\sqrt{5}\)+ 2 - \(2\sqrt{5}\)+1
= 3
B = \(\frac{\left(1-\sqrt{x}\right)^2+4\sqrt{x}}{1+\sqrt{x}}\)( x \(\ge\)0 )
= \(\frac{1-2\sqrt{x}+x+4\sqrt{x}}{1+\sqrt{x}}\)
= \(\frac{1+2\sqrt{x}+x}{1+\sqrt{x}}\)
= \(\frac{\left(1+\sqrt{x}\right)^2}{1+\sqrt{x}}\)
= 1 +\(\sqrt{x}\)
#mã mã#
NV
Nguyễn Việt Lâm
Giáo viên
7 tháng 5 2023
\(5\sqrt{\left(-2\right)^4}=5\sqrt{4^2}=5.4=20\)
\(-4\sqrt{\left(-3\right)^6}=-4\sqrt{27^2}=-4.27=-108\)
\(\sqrt{\sqrt{\left(-5\right)^8}}=\sqrt{\sqrt{\left(5^4\right)^2}}=\sqrt{5^4}=\sqrt{25^2}=25\)
23 tháng 8 2017
mik làm bài này
linh tinh
bn ơi
cho mik
xin 1 L-I-K-E
b,
d,
22 tháng 8 2017
\(\sqrt{\frac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\frac{4}{\left(2+\sqrt{5}\right)^2}}\)
\(=\frac{2}{\sqrt{5}-2}-\frac{2}{2+\sqrt{5}}\)
\(=\frac{2\left(\sqrt{5}+2\right)-2\left(\sqrt{5}-2\right)}{5-4}\)
\(=2\sqrt{5}+4-2\sqrt{5}+4\)
\(=8\)
18 tháng 9 2019
d/ \(x=\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}\)
\(\Leftrightarrow x^3=3+\sqrt{9+\frac{125}{27}}+3-\sqrt{9+\frac{125}{27}}-3\left(\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}\right)\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}.\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}\)
\(\Leftrightarrow x^3=6-3x\sqrt[3]{9-9-\frac{125}{27}}\)
\(\Leftrightarrow x^3=6-5x\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+6\right)=0\)
\(\Leftrightarrow x=1\)
19 tháng 9 2019
c/
\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{\left(4-\sqrt{2}\right)^2}}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{12}+4}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{2-\sqrt{3}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)
\(=3-1=2\)
20 tháng 6 2017
\(A=\frac{\sqrt{7-2\sqrt{10}}.\left(7+2\sqrt{10}\right)\left(74-22\sqrt{10}\right)}{\sqrt{125}-4\sqrt{50}+5\sqrt{20}+\sqrt{8}}\)
\(=\frac{\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}.\left(78-6\sqrt{10}\right)}{5\sqrt{5}-20\sqrt{2}+10\sqrt{5}+2\sqrt{2}}\)
\(=\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(78-6\sqrt{10}\right)}{15\sqrt{5}-18\sqrt{2}}\)
\(=\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(26-2\sqrt{10}\right)}{5\sqrt{5}-6\sqrt{2}}\)
\(=\frac{30\sqrt{5}-36\sqrt{2}}{5\sqrt{5}-6\sqrt{2}}=6\)
Nhầm nha mn
\(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
\(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
\(=\frac{5+4+4\sqrt{5}-8\sqrt{5}}{2\sqrt{5}-4}\)
\(=\frac{9-4\sqrt{5}}{2\sqrt{5}-4}\)
\(=\frac{\sqrt{5}^2-4\sqrt{5}+2^2}{2\sqrt{5}-4}\)
\(=\frac{\left(\sqrt{5}-2\right)^2}{2\left(\sqrt{5}-2\right)}\)
\(=\frac{\sqrt{5}-2}{2}\)