(14/√14 + √12+√30 / √2+√5 ) . √5-√21 = 4
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TQ
1
AD
25 tháng 7 2023
\(VT=\left(\dfrac{\sqrt{14}.\sqrt{14}}{\sqrt{14}}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right)\sqrt{5-\sqrt{21}}\\ =\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\\ =\sqrt{14}.\sqrt{5-\sqrt{2}1}+\sqrt{6}.\sqrt{5-\sqrt{21}}\\ =\sqrt{70-14\sqrt{21}}+\sqrt{30-6\sqrt{21}}\\ =\sqrt{49-2.7.\sqrt{21}+21}+\sqrt{9-2.3.\sqrt{21}+21}\\ =\sqrt{\left(7-\sqrt{21}\right)^2}+\sqrt{\left(3-\sqrt{21}\right)^2}\\ =\left|7-\sqrt{21}\right|+\left|3-\sqrt{21}\right|\\ =7-\sqrt{21}+\sqrt{21}-3\\ =7-3=4=VP\)
29 tháng 6 2021
\(VT=\left(\dfrac{\sqrt{14.14}}{\sqrt{14}}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
\(=\sqrt{30-6\sqrt{21}}+\sqrt{70-14\sqrt{21}}\)
\(=\sqrt{21-2.3\sqrt{21}+9}+\sqrt{21-2.7.\sqrt{21}+49}\)
\(=\sqrt{\left(\sqrt{21}-3\right)^2}+\sqrt{\left(7-\sqrt{21}\right)^2}\)
\(=\sqrt{21}-3+7-\sqrt{21}=4\)
CS
20 tháng 10 2021
a) \(=2\sqrt{5}-3\sqrt{5}+\sqrt{5}-1=-1\)
b) \(=\left[\sqrt{14}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right].\sqrt{\left(\sqrt{\dfrac{7}{2}}-\sqrt{\dfrac{3}{2}}\right)^2}\)
\(=\left(\sqrt{14}+\sqrt{6}\right)\left(\sqrt{\dfrac{7}{2}}-\sqrt{\dfrac{3}{2}}\right)\)
\(=\sqrt{49}-\sqrt{21}+\sqrt{21}-\sqrt{9}\)
\(=7-3=4\)
2 tháng 4 2021
c) Ta có: \(\dfrac{3}{5}+\dfrac{-5}{20}+\dfrac{30}{75}+\dfrac{-7}{4}\)
\(=\dfrac{3}{5}+\dfrac{2}{5}+\dfrac{-1}{4}+\dfrac{-7}{4}\)
\(=1-2=-1\)
2 tháng 4 2021
Giải:
a)-1/12+4/3=-1/12+16/12=15/12=5/4
b)(-4/14-3/15)-(1/5-20/35-(-1)).7
=-17/35-22/35.7
=-17/35-22/5
=-171/35
c)3/5+-5/20+30/75+-7/4
=3/5+-1/4+2/5+-7/4
=(3/5+2/5)+(-1/4+-7/4)
=1+-2
=-1
d)5/6.-12/14+7/13
=-5/7+7/13
=-16/91
e)2/-9-5/-36-1/4
=-1/12-1/4
=-1/3
f)2/23+-5/12+7/18+21/23+-7/12
=(2/23+21/23)+(-5/12+-7/12)+7/18
=1+-1+7/18
=7/18
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
19 tháng 9 2015
\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)
\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)
\(4^{21}=\left(4^3\right)^7=64^7>64^2\)
\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)
\(31^{11}<32^{11}=\left(2^5\right)^{11}=2^{55}\)
\(17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\)
\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)
Các bài khác làm tương tự
Ta có: \(\left(\dfrac{14}{\sqrt{14}}+\dfrac{\sqrt{12}+\sqrt{30}}{\sqrt{2}+\sqrt{5}}\right)\cdot\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{14}+\sqrt{6}\right)\cdot\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
=7-3
=4