Tính \(T=\frac{4+\sqrt{7}}{2\sqrt{2}+\sqrt{4+\sqrt{7}}}+\frac{4-\sqrt{7}}{2\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
Những câu hỏi liên quan
Tính GTBT:
\(B=\frac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\frac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
B = \(\frac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\frac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
=> \(\frac{2}{\sqrt{2}}B=\frac{8+2\sqrt{7}}{6+\sqrt{8+2\sqrt{7}}}+\frac{8-2\sqrt{7}}{6-\sqrt{8-2\sqrt{7}}}\)
=> \(\frac{2}{\sqrt{2}}B=\frac{\left(\sqrt{7}+1\right)^2}{6+\sqrt{7}+1}+\frac{\left(\sqrt{7}-1\right)^2}{6-\sqrt{7}+1}\)
=> \(\frac{2}{\sqrt{2}}B=\frac{\left(\sqrt{7}+1\right)^2}{\sqrt{7}\left(\sqrt{7}+1\right)}+\frac{\left(\sqrt{7}-1\right)^2}{\sqrt{7}\left(\sqrt{7}-1\right)}\)
=> \(\frac{2}{\sqrt{2}}B=\frac{\sqrt{7}+1}{\sqrt{7}}+\frac{\sqrt{7}-1}{\sqrt{7}}=\frac{2\sqrt{7}}{\sqrt{7}}=2\)
=> B = \(\sqrt{2}\)
Đúng 0
Bình luận (0)
Tính
1, a = \(\sqrt[3]{45+26\sqrt{2}}+\sqrt[3]{45-29\sqrt{2}}\)
2, x = \(\sqrt[3]{4+\sqrt{80}-\sqrt[3]{\sqrt{80}-4}}\)
3, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
4, \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
5, \(\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}+\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}\)
Tính GTBT:
\(B=\frac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\frac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
\(B=\frac{\sqrt{2}\left(4+\sqrt{7}\right)}{6+\sqrt{8+2\sqrt{7}}}+\frac{\sqrt{2}\left(4-\sqrt{7}\right)}{6-\sqrt{8-2\sqrt{7}}}=\frac{\sqrt{2}\left(4+\sqrt{7}\right)}{6+\sqrt{\left(\sqrt{7}+1\right)^2}}+\frac{\sqrt{2}\left(4-\sqrt{7}\right)}{6-\sqrt{\left(\sqrt{7}-1\right)^2}}\)
\(=\frac{\sqrt{2}\left(4+\sqrt{7}\right)}{7+\sqrt{7}}+\frac{\sqrt{2}\left(4-\sqrt{7}\right)}{7-\sqrt{7}}=\frac{\sqrt{2}\left(4+\sqrt{7}\right)\left(7-\sqrt{7}\right)}{35}+\frac{\sqrt{2}\left(4-\sqrt{7}\right)\left(7+\sqrt{7}\right)}{35}\)
\(=\frac{21\sqrt{2}+3\sqrt{14}}{35}+\frac{21\sqrt{2}-3\sqrt{14}}{35}=\frac{42\sqrt{2}}{35}=\frac{6\sqrt{2}}{5}\)
Đúng 0
Bình luận (0)
sqrt{4-sqrt{7}}-sqrt{4+sqrt{7}}+sqrt{2}sqrt{frac{2left(4-sqrt{7}right)}{2}}-sqrt{frac{2left(4+sqrt{7}right)}{2}}+sqrt{2}sqrt{frac{8-2sqrt{7}}{2}}-sqrt{frac{8+2sqrt{7}}{2}}+sqrt{2}sqrt{frac{left(sqrt{7}-1right)^2}{2}}-sqrt{frac{left(sqrt{7}+1right)^2}{2}}+sqrt{2}frac{sqrt{7}-1}{sqrt{2}}-frac{sqrt{7}+1}{sqrt{2}}+sqrt{2}frac{-2}{sqrt{2}}+sqrt{2}-sqrt{2}+sqrt{2}0
Đọc tiếp
\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2}=\sqrt{\frac{2\left(4-\sqrt{7}\right)}{2}}-\sqrt{\frac{2\left(4+\sqrt{7}\right)}{2}}+\sqrt{2}\)
=\(\sqrt{\frac{8-2\sqrt{7}}{2}}-\sqrt{\frac{8+2\sqrt{7}}{2}}+\sqrt{2}\)
=\(\sqrt{\frac{\left(\sqrt{7}-1\right)^2}{2}}-\sqrt{\frac{\left(\sqrt{7}+1\right)^2}{2}}+\sqrt{2}\)
=\(\frac{\sqrt{7}-1}{\sqrt{2}}-\frac{\sqrt{7}+1}{\sqrt{2}}+\sqrt{2}\)
=\(\frac{-2}{\sqrt{2}}+\sqrt{2}\)
=\(-\sqrt{2}+\sqrt{2}\)
=0
Tính:
\(a,\frac{2}{4-3\sqrt{2}}-\frac{2}{4+3\sqrt{2}}\)
\(b,\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
a) \(\frac{2}{4-3\sqrt{2}}-\frac{2}{4+3\sqrt{2}}\)
\(=\frac{2\left(4+3\sqrt{2}\right)}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}-\frac{2\left(4-3\sqrt{2}\right)}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}\)
\(=\frac{2\left(4+3\sqrt{2}\right)-2\left(4-3\sqrt{2}\right)}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}\)
\(=\frac{12\sqrt{2}}{-2}\)
\(=-6\sqrt{2}\)
b) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
\(=\frac{\left(\sqrt{7}+\sqrt{5}\right)^2}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}-\frac{\left(\sqrt{7}-\sqrt{5}\right)^2}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}\)
\(=\frac{\left(\sqrt{7}+\sqrt{5}\right)^2-\left(\sqrt{7}-\sqrt{5}\right)^2}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}\)
\(=\frac{4\sqrt{35}}{2}\)
\(=2\sqrt{35}\)
Đúng 0
Bình luận (0)
tính
a, \(A=2\sqrt{12}-3\sqrt{48}+4\sqrt{75}\)
\(B=\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}+\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}\)
c, \(C=\frac{3-2\sqrt{3}}{\sqrt{3}}+\frac{6}{3+\sqrt{3}}\)
d,
a) A=12\(\sqrt{3}\)
B= \(\frac{8}{3}\)
c) C= 1
d)...
Chúc bạn học tốt nha ^^!
Đúng 0
Bình luận (0)
Tính:
\(a)\sqrt{4-2\sqrt{3}}+\sqrt{7-4\sqrt{3}}\\ b)\frac{6}{\sqrt{7}+2}+\sqrt{\frac{2}{8+3\sqrt{7}}}\)
\(y=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{4+\sqrt{3}}{5-2\sqrt{3}}}-\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{4}}}\)
Mọi người giải hộ mình nhé. Tính giá trị biểu thức trên
tính:\(\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{9}}\)