\(\dfrac{4}{\sqrt{5}-1}+\dfrac{3}{\sqrt{5}-2}-\dfrac{16}{3-\sqrt{5}}\)
\(=\sqrt{5}+1+3\sqrt{5}+6-12-4\sqrt{5}\)
=-5
Đúng 2
Bình luận (1)
Violympic toán 9
Các câu hỏi tương tự
So sánh 2 số: \(R=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(S=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
So sánh 2 số: \(R=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(S=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
Rút gọn các biểu thức :
A=\(\dfrac{1}{\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}}\)
B= \(\dfrac{1}{1+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+...+\dfrac{1}{\sqrt{2015}+\sqrt{2017}}\)
2 . rút gọn biểu thức
a. sqrt{200}-sqrt{32}+sqrt{72}
b. sqrt{175}-sqrt{112}+sqrt{63}
c. dfrac{3}{2}sqrt{6}+2sqrt{dfrac{2}{3}}-4sqrt{dfrac{3}{2}}
d. 4sqrt{20}-3sqrt{125}+5sqrt{45}-15sqrt{dfrac{1}{5}}
e. 5sqrt{dfrac{1}{5}+}dfrac{1}{5}sqrt{20}+sqrt{5}
f. sqrt{dfrac{1}{5}}+sqrt{4,5}+sqrt{12,5}
g. dfrac{1}{2}sqrt{48}-2sqrt{75}-sqrt{54}+5sqrt{1dfrac{1}{3}}
m. 3sqrt{5a}-sqrt{20a}+sqrt{a}+4sqrt{45a}
n. 3sqrt{8}-sqrt{18}-5sqrt{dfrac{1}{2}}+sqrt{50}
i. sqrt{72}+sqrt{4dfrac{1}{2}}-sqrt{32}+sqrt{6...
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2 . rút gọn biểu thức
a. \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)
b. \(\sqrt{175}-\sqrt{112}+\sqrt{63}\)
c. \(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\)
d. \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)
e. \(5\sqrt{\dfrac{1}{5}+}\dfrac{1}{5}\sqrt{20}+\sqrt{5}\)
f. \(\sqrt{\dfrac{1}{5}}+\sqrt{4,5}+\sqrt{12,5}\)
g. \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\sqrt{54}+5\sqrt{1\dfrac{1}{3}}\)
m. \(3\sqrt{5a}-\sqrt{20a}+\sqrt{a}+4\sqrt{45a}\)
n. \(3\sqrt{8}-\sqrt{18}-5\sqrt{\dfrac{1}{2}}+\sqrt{50}\)
i. \(\sqrt{72}+\sqrt{4\dfrac{1}{2}}-\sqrt{32}+\sqrt{63}-\sqrt{162}\)
Chứng minh: \(\dfrac{\sqrt[4]{5}-1}{\sqrt[4]{5}+1}=\sqrt[4]{\dfrac{3+2\sqrt[4]{5}}{3-2\sqrt[4]{5}}}\)
Giải phương trình:
1. sqrt{2x^2+4x+7}x^4+4x^3+3x^2-2x-7
2. dfrac{4}{x}+sqrt{x-dfrac{1}{x}}x+sqrt{2x-dfrac{5}{x}}
3. dfrac{6-2x}{sqrt{5-x}}+dfrac{6+2x}{sqrt{5+x}}dfrac{8}{3}
4. x^2+1-left(x+1right)sqrt{x^2-2x+3}0
5. 2sqrt{2x+4}+4sqrt{2-x}sqrt{9x^2+16}
6. left(2x+7right)sqrt{2x+7}x^2+9x+7
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Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
cmr:
\(\dfrac{1}{\sqrt{3}}\)+\(\dfrac{1}{3\sqrt{2}}\)+\(\dfrac{1}{\sqrt{3}}\).\(\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)=\(\dfrac{\sqrt{3}}{2}\)
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giúp mk tính
a,sqrt{5}-sqrt{48}+5sqrt{27}-sqrt{45}
b,(sqrt{5}+sqrt{2}) (3sqrt{2}-1)
c,3sqrt{50}-2sqrt{75}-4dfrac{sqrt{54}}{sqrt{3}}-3sqrt{dfrac{1}{3}}
d, sqrt{left(sqrt{3}-3right)^2}+sqrt{4-2sqrt{3}}
e, sqrt{48-2sqrt{135}}-sqrt{45}+sqrt{18}
f, dfrac{5sqrt{2}-2sqrt{5}}{sqrt{5}-sqrt{2}}+dfrac{6}{2-sqrt{10}}-dfrac{20}{sqrt{10}}
bài 2
a, sqrt{9-4sqrt{5}}
b,2sqrt{3}+sqrt{48}-sqrt{75}-sqrt{243}
csqrt{4+sqrt{8}}.sqrt{2+sqrt{2+sqrt{2}}}.sqrt{2-sqrt{2+sqrt{2}}}
d, sqrt{3+2sqrt{2}}-sqrt{6-4sqr...
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giúp mk tính
a,\(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)
b,(\(\sqrt{5}+\sqrt{2}\)) (\(3\sqrt{2}-1\))
c,\(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
d, \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)
e, \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
f, \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
bài 2
a, \(\sqrt{9-4\sqrt{5}}\)
b,\(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
c\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
d, \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
e,\(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)+\(\dfrac{\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)
f, \(\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
CM: \(\left(\dfrac{2}{\sqrt{6}-1}+\dfrac{3}{\sqrt{6}-2}+\dfrac{3}{\sqrt{6}-3}\right).\dfrac{5}{9\sqrt{6}+4}=\dfrac{1}{2}\)