\(n=\frac{\left(127+24\sqrt{28}\right)^k-\left(127-24\sqrt{28}\right)^k}{2\sqrt{28}}\)
K
Khách
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AT
2 tháng 7 2021
a) \(\left(\sqrt{28}-5\sqrt{35}+7\sqrt{112}\right)2\sqrt{7}=2\sqrt{196}-10\sqrt{245}+14\sqrt{784}\)
\(=28-10\sqrt{49.5}+392=420-70\sqrt{5}\)
b) \(\left(\sqrt{72}-3\sqrt{24}+5\sqrt{8}\right)\sqrt{2}+4\sqrt{27}=\sqrt{144}-3\sqrt{48}+5\sqrt{16}+4\sqrt{9.3}\)
\(=12-3\sqrt{16.3}+20+12\sqrt{3}=32-12\sqrt{3}+12\sqrt{3}=32\)
2 tháng 3 2018
thay 28 vao pt nhan tu roi am-gm cho cai do luon
Ps: tim Min
5 tháng 4 2021
a) Ta có: \(M=\dfrac{2}{\sqrt{7}-\sqrt{6}}-\sqrt{28}+\sqrt{54}\)
\(=\dfrac{2\left(\sqrt{7}+\sqrt{6}\right)}{\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right)}-2\sqrt{7}+3\sqrt{6}\)
\(=2\sqrt{7}+2\sqrt{6}-2\sqrt{7}+3\sqrt{6}\)
\(=5\sqrt{6}\)
5 tháng 4 2021
b) Ta có: \(N=\left(2-\sqrt{3}\right)\left(\sqrt{26+15\sqrt{3}}\right)-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{52+30\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{52-30\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{27+2\cdot3\sqrt{3}\cdot5+25}-\left(2+\sqrt{3}\right)\sqrt{27-2\cdot3\sqrt{3}\cdot5+25}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\sqrt{\left(3\sqrt{3}+5\right)^2}-\left(2+\sqrt{3}\right)\sqrt{\left(3\sqrt{3}-5\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\left(2-\sqrt{3}\right)\left(3\sqrt{3}+5\right)-\left(2+\sqrt{3}\right)\left(3\sqrt{3}-5\right)}{\sqrt{2}}\)
\(=\dfrac{6\sqrt{3}+10-9-5\sqrt{3}-\left(6\sqrt{3}-10+9-5\sqrt{3}\right)}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1-\sqrt{3}+1}{\sqrt{2}}\)
\(=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
KH
22 tháng 8 2019
\(a.\\ \left(\sqrt{4.3}-\sqrt{16.3}-\sqrt{36.3}-\sqrt{64.3}\right)\\ =\left(2\sqrt{3}-4\sqrt{3}-6\sqrt{3}-8\sqrt{3}\right):2\sqrt{3}\\ =\frac{-16\sqrt{3}}{2\sqrt{3}}=-8\)
\(b.\\ =\left(2\sqrt{16.7}-5\sqrt{7}+2\sqrt{9.7}-2\sqrt{4.7}\right)\sqrt{7}\\ =\left(8\sqrt{7}-5\sqrt{7}+6\sqrt{7}-4\sqrt{7}\right)\sqrt{7}\\ =5\sqrt{7}.\sqrt{7}=5.7=35\)
\(c.\\ =\left(2\sqrt{9.3}-3\sqrt{16.3}+3\sqrt{25.3}-\sqrt{64.3}\right)\left(1-\sqrt{3}\right)\\ =\left(6\sqrt{3}-12\sqrt{3}+15\sqrt{3}-8\sqrt{3}\right)\left(1-\sqrt{3}\right)\\ =\sqrt{3}\left(1-\sqrt{3}\right)\\ =\sqrt{3}-3\)
\(d.\\ =7\sqrt{4.6}-\sqrt{25.6}-5\sqrt{9.6}\\ =14\sqrt{6}-5\sqrt{6}-15\sqrt{6}=-6\sqrt{6}\)
23 tháng 3 2019
mik ko ghi lại đề nhé!
\(A=\left(\frac{18}{15}.\frac{1}{4}.3\right)+\left(-\frac{47}{60}\right).\frac{24}{47}\)
\(A=\frac{8}{5}+\left(-\frac{2}{5}\right)\)
\(A=\frac{6}{5}\)
23 tháng 3 2019
\(B=\frac{3}{4}.\frac{28}{15}-\left(\frac{8}{15}+\frac{1}{4}\right).\frac{24}{47}-\frac{17}{13}\)
\(B=\frac{7}{5}-\frac{47}{60}.\frac{24}{47}-\frac{17}{13}\)
\(B=\frac{7}{5}-\frac{2}{5}-\frac{17}{13}\)
\(B=1-\frac{17}{13}\)
\(B=-\frac{4}{13}\)
THANKS