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13 tháng 10 2019

=\(\frac{10\left(\sqrt{4}-1\right)}{4-1}+\frac{10\left(\sqrt{7}-1\right)}{7-4}+\frac{10\left(\sqrt{10}-\sqrt{7}\right)}{10-7}+...+\frac{10\left(\sqrt{100}-\sqrt{97}\right)}{100-97}\)

=\(\frac{10}{3}+\frac{10\sqrt{7}-10}{3}+\frac{10\sqrt{10}-10\sqrt{7}}{3}+...+\frac{10\sqrt{100}-10\sqrt{97}}{3}\)

=\(\frac{1}{3}\left(10+10\sqrt{7}-10+10\sqrt{10}-10\sqrt{7}+...+10\sqrt{100}-10\sqrt{97}\right)\)

=\(\frac{1}{3}\left(10\sqrt{100}-10\right)\)

=30

12 tháng 10 2019

\(\frac{10}{\sqrt{a}+\sqrt{a+3}}=\frac{10\left(\sqrt{a+3}-\sqrt{a}\right)}{\left(\sqrt{a+3}+\sqrt{a}\right)\left(\sqrt{a+3}-\sqrt{a}\right)}=\frac{10}{3}\left(\sqrt{a+3}-\sqrt{a}\right)\)

6 tháng 9 2019

help me

=10( (1-√4)/(1-4) + (√4-√7)/(4-7)+.....+(√97-√100)/(97-100) )

=10 (1-100)/3

=-990/3 = -330

Mik cx l9 

k hay ko tùy bn

19 tháng 8 2020

\(a,\frac{6}{4+\sqrt{4-2\sqrt{3}}}=\frac{6}{4+\sqrt{\sqrt{3}^2-2\sqrt{3}+\sqrt{1}^2}}\)

\(=\frac{6}{4+\sqrt{\left(\sqrt{3}-\sqrt{1}\right)^2}}=\frac{6}{4+|\sqrt{3}-1|}=\frac{6}{3+\sqrt{3}}\)

\(=\frac{6}{\sqrt{3}\left(\sqrt{3}+1\right)}=\frac{\sqrt{36}}{\sqrt{3}\left(\sqrt{3}+1\right)}=\frac{\sqrt{3}.\sqrt{12}}{\sqrt{3}\left(\sqrt{3}+1\right)}=\frac{\sqrt{12}}{\sqrt{3}+1}\)

\(d,\frac{1}{\sqrt{7-2\sqrt{10}}}+\frac{1}{\sqrt{7+2\sqrt{10}}}\)

\(=\frac{1}{\sqrt{\sqrt{5}^2-2.\sqrt{2}.\sqrt{5}+\sqrt{2}^2}}+\frac{1}{\sqrt{\sqrt{5}^2+2.\sqrt{2}.\sqrt{5}+\sqrt{2}^2}}\)

\(=\frac{1}{\sqrt{\left(\sqrt{5}-\sqrt{2}\right)}}+\frac{1}{\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}}\)

\(=\frac{1}{\sqrt{5}-\sqrt{2}}+\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}+\sqrt{2}+\sqrt{5}-\sqrt{2}}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}\)

\(=\frac{2\sqrt{5}}{\sqrt{5}^2-\sqrt{2}^2}=\frac{\sqrt{5.4}}{5-2}=\frac{\sqrt{20}}{3}\)

22 tháng 10 2021

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+2\sqrt{12}}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-2\sqrt{75}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)

\(C=\sqrt{4+5}\)

\(C=3\)