Các câu hỏi tương tự
Bài 1:a, Asqrt{2-sqrt{3}}+sqrt{2+sqrt{3}}b, B left(frac{1}{sqrt{5}-sqrt{2}}-frac{1}{sqrt{5}+sqrt{2}}+1right).frac{1}{left(sqrt{2}+1right)^2}Bài 2: Giải pta,frac{5sqrt{x}-2}{8sqrt{x}+2,5}frac{2}{7}b, sqrt{x^2-6x+9}sqrt{4+2sqrt{3}}Bài 3:Aleft(frac{x+2}{xsqrt{x}+1}-frac{1}{sqrt{x}+1}right).frac{4sqrt{x}}{3}
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Bài 1:
a, A=\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
b, B= \(\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right).\frac{1}{\left(\sqrt{2}+1\right)^2}\)
Bài 2: Giải pt
a,\(\frac{5\sqrt{x}-2}{8\sqrt{x}+2,5}=\frac{2}{7}\)
b, \(\sqrt{x^2-6x+9}=\sqrt{4+2\sqrt{3}}\)
Bài 3:
A=\(\left(\frac{x+2}{x\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\right).\frac{4\sqrt{x}}{3}\)
tìm x để biểu thức có nghĩaAfrac{x+1}{sqrt{x-2}}Bsqrt{9-x^2}+frac{1}{x-2}Csqrt{-6x^2}+sqrt{1-x^2}Dfrac{sqrt{x-1}+sqrt{x-2}}{sqrt{x^2}-4left(x-1right)}Efrac{15sqrt{x}-11}{x+2sqrt{x}-3}-frac{3sqrt{x}-2}{sqrt{x}-1}-frac{2sqrt{x}+3}{sqrt{x+3}}Fsqrt{x^2-6x+9}+sqrt{x-2sqrt{x-1}}
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tìm x để biểu thức có nghĩa
\(A=\frac{x+1}{\sqrt{x-2}}\)
\(B=\sqrt{9-x^2}+\frac{1}{x-2}\)
\(C=\sqrt{-6x^2}+\sqrt{1-x^2}\)
\(D=\frac{\sqrt{x-1}+\sqrt{x-2}}{\sqrt{x^2}-4\left(x-1\right)}\)
\(E=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x+3}}\)
\(F=\sqrt{x^2-6x+9}+\sqrt{x-2\sqrt{x-1}}\)
1) Rút gọn biểu thức: a, sqrt{2+sqrt{3}}-sqrt{2-sqrt{3}} b, sqrt{4-sqrt{7}}+sqrt{4+sqrt{7}}2) Giải phương trình: a, left(xsqrt{frac{6}{x}}+sqrt{frac{2x}{3}}+sqrt{6x}right).sqrt{6x}2 b, left(sqrt{frac{3}{x}}+sqrt{frac{x}{3}}+sqrt{3x}right).sqrt{3x}3 c, sqrt{x^2+2x+1}-sqrt{x^2-1}0 d, sqrt{x}+sqrt{x+1}frac{1}{sqrt{x}}
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1) Rút gọn biểu thức:
a, \(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
b, \(\sqrt{4-\sqrt{7}}+\sqrt{4+\sqrt{7}}\)
2) Giải phương trình:
a, \(\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}\right).\sqrt{6x}=2\)
b, \(\left(\sqrt{\frac{3}{x}}+\sqrt{\frac{x}{3}}+\sqrt{3x}\right).\sqrt{3x}=3\)
c, \(\sqrt{x^2+2x+1}-\sqrt{x^2-1}=0\)
d, \(\sqrt{x}+\sqrt{x+1}=\frac{1}{\sqrt{x}}\)
giúp vs1)a) n thuộc N*: rút gọn:K sqrt{1+frac{1}{n^2}+frac{1}{left(n+1right)^2}}b) tínhI sqrt{1+frac{1}{1^2}+frac{1}{2^2}}+sqrt{1+frac{1}{2^2}+frac{1}{3^2}}+sqrt{1+frac{1}{3^2}+frac{1}{4^2}}+...+sqrt{1+frac{1}{2015^2}+frac{1}{2016^2}}+sqrt{1+frac{1}{2016^2}+frac{1}{2017^2}}2) A sqrt{x^2-6x+9}-sqrt{x^2+6x+9}a) rút gọn Ab) tìm x đề A13) rút gọn B sqrt{x+sqrt{2x-1}}-sqrt{x-sqrt{2x-1}}4) tính: frac{sqrt{sqrt{5}+2}+sqrt{sqrt{5}-2}}{sqrt{sqrt{5}+1}}-sqrt{3-2sqrt{2}}C sqrt{4+sqrt{10+2sqrt{5}}}+sqrt{...
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giúp vs
1)a) n thuộc N*: rút gọn:
K = \(\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}\)
b) tính
I = \(\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2015^2}+\frac{1}{2016^2}}+\sqrt{1+\frac{1}{2016^2}+\frac{1}{2017^2}}\)2) A= \(\sqrt{x^2-6x+9}-\sqrt{x^2+6x+9}\)
a) rút gọn A
b) tìm x đề A=1
3) rút gọn B = \(\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\)
4) tính: \(\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
C= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
giải phương trìnha) left(x+frac{5-x}{sqrt{x}+1}right)^2+frac{16sqrt{x}left(5-xright)}{sqrt{x}+1}-160b) sqrt{2x-frac{3}{x}}+sqrt{frac{6}{x}-2x}1+frac{3}{2x}c) sqrt{2x+1}+frac{2x-1}{x+3}-left(2x-1right)sqrt{x^2+4}-sqrt{2}0d) sqrt{x+2+3sqrt{2x-5}}+sqrt{x-2-sqrt{2x-5}}2sqrt{2}
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giải phương trình
a) \(\left(x+\frac{5-x}{\sqrt{x}+1}\right)^2+\frac{16\sqrt{x}\left(5-x\right)}{\sqrt{x}+1}-16\)\(=0\)
b) \(\sqrt{2x-\frac{3}{x}}+\sqrt{\frac{6}{x}-2x}=1+\frac{3}{2x}\)
c) \(\sqrt{2x+1}+\frac{2x-1}{x+3}-\left(2x-1\right)\sqrt{x^2+4}-\sqrt{2}=0\)
d) \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
Rút gọn các biểu thức sau:a.frac{1}{sqrt{2}-sqrt{3}}-sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}} b.sqrt{frac{4}{left(2-sqrt{5}right)^2}}-sqrt{frac{4}{left(2+sqrt{5}right)^2}}c.sqrt{frac{3+2sqrt{2}}{3-2sqrt{2}}}+sqrt{frac{sqrt{2}-1}{sqrt{2}+1}} d.frac{1}{sqrt{5}-2}.sqrt{frac{2sqrt{5}-4}{2sqrt{5}+4}}e.x+1-sqrt{x^2-2x+1}left(x1right) f.3x+sqrt{9x^2+6x+1}left(x frac{1}{3}right)g.frac{1}{9x^2-1}.sqrt{1-6x+9x^2}left(x frac{1}{3}right) h.frac{a-b}{3b}.sqrt{frac{4a^2...
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Rút gọn các biểu thức sau:
\(a.\frac{1}{\sqrt{2}-\sqrt{3}}-\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\) \(b.\sqrt{\frac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\frac{4}{\left(2+\sqrt{5}\right)^2}}\)
\(c.\sqrt{\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}+\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}\) \(d.\frac{1}{\sqrt{5}-2}.\sqrt{\frac{2\sqrt{5}-4}{2\sqrt{5}+4}}\)
\(e.x+1-\sqrt{x^2-2x+1}\left(x>=1\right)\) \(f.3x+\sqrt{9x^2+6x+1}\left(x< \frac{1}{3}\right)\)
\(g.\frac{1}{9x^2-1}.\sqrt{1-6x+9x^2}\left(x< =\frac{1}{3}\right)\) \(h.\frac{a-b}{3b}.\sqrt{\frac{4a^2b^4}{a^2-2ab+b^2}}\left(a< b< 0\right)\)
chứng minh \(\left(x\sqrt{\frac{^6}{x}}+\sqrt{\frac{2x}{3}}-\sqrt{6x}\right)\div\sqrt{6x}=2\frac{1}{3}\)
với x lớn hơn 0.
Chứng minh các đẳng thức sau:
a) \(\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-4\sqrt{\frac{3}{2}}=\frac{\sqrt{6}}{6}\)
b) \(\left(x\sqrt{\frac{6}{x}}+\sqrt{\frac{2X}{3}}+\sqrt{6X}\right):\sqrt{6X}=2\frac{1}{3}\)với x > 0
Giải phương trình: 1)sqrt{9x^2-15x+9}+sqrt{x^3+3x^2-3x+1}+x22)sqrt{3x^2-1}+sqrt{x^2-x}-xsqrt{x^2+1}frac{1}{2sqrt{2}}3)sqrt{-4x^4y^2+16x^2y+9}-sqrt{x^2y^2-2y^2}2left(x^2+frac{1}{x^2}right)left(vớix0right)4)x^3-3x^2+2sqrt{left(x+2right)^3}-6x05)4x^2-11x+10left(x+1right)sqrt{2x^2-6x+2}
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Giải phương trình:
1)\(\sqrt{9x^2-15x+9}+\sqrt{x^3+3x^2-3x+1}+x=2\)
2)\(\sqrt{3x^2-1}+\sqrt{x^2-x}-x\sqrt{x^2+1}=\frac{1}{2\sqrt{2}}\)
3)\(\sqrt{-4x^4y^2+16x^2y+9}-\sqrt{x^2y^2-2y^2}=2\left(x^2+\frac{1}{x^2}\right)\left(vớix>0\right)\)
4)\(x^3-3x^2+2\sqrt{\left(x+2\right)^3}-6x=0\)
5)\(4x^2-11x+10=\left(x+1\right)\sqrt{2x^2-6x+2}\)