\(\sqrt{\frac{6}{2-x}}+\sqrt{\frac{10}{3-x}}=4\)
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#mã mã#
Những câu hỏi liên quan
Giai các bất phương trình sau :
a/ \(\frac{\sqrt{x^2-4x}}{3-x}\le2\)
b/ \(\frac{\sqrt{-2x^2-15x+17}}{x+3}\ge0\)
c/ \(\left(x+3\right)\sqrt{x^2-4}\le x^2-9\)
d/ \(\frac{\sqrt{-x^2+x+6}}{2x+5}\ge\frac{\sqrt{-x^2+x+6}}{x+4}\)
HELP ME !!!!!
Please help me, chiều nay 5h tui đi học rùi . Giải giúp tui ik mừ.
Giải phương trình :
\(a,\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=\sqrt{1+2020^2+\frac{2020^2}{2021^2}}+\frac{2020}{2021}\)
\(b,\sqrt{x+2+2\sqrt{x+1}}+\sqrt{x+10-6\sqrt{x+1}}=2\sqrt{x+2-2\sqrt{x+1}}\)
\(c,\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x+\frac{3}{2}\)
Rút gọn biểu thức :
E=\(\frac{\sqrt{2x+2\sqrt{x^2-4}}}{\sqrt{x^2-4}+x+2}\)
F=\(\frac{\left(\frac{3}{\sqrt{1+a}}+\sqrt{1+a}\right)}{\left(\frac{3}{\sqrt{1-a^2}}+1\right)}\)
HELP ME !
ĐKXĐ:...
\(E=\frac{\sqrt{x+2+2\sqrt{\left(x+2\right)\left(x-2\right)}+x-2}}{\sqrt{\left(x+2\right)\left(x-2\right)}+x+2}\)
\(=\frac{\sqrt{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}}{\sqrt{x+2}\left(\sqrt{x-2}+\sqrt{x+2}\right)}=\frac{1}{\sqrt{x+2}}\)
Câu sau đề đúng ko bạn? Thế này thì ko rút gọn được, tử số là \(\frac{3}{\sqrt{1+a}}+\sqrt{1-a}\) thì mới rút được
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1)rút gọn
a) \(\frac{2}{3}\sqrt{3}-\frac{1}{4}\sqrt{18}+\frac{2}{5}\sqrt{2}-\frac{1}{4}\sqrt{12}\)
b) (\(\sqrt{10}+\sqrt{2}\))(6-2\(\sqrt{5}\))\(\sqrt{3+\sqrt{5}}\)
help me
a) \(\frac{2}{3}\sqrt{3}-\frac{1}{4}\sqrt{18}+\frac{2}{5}\sqrt{2}-\frac{1}{4}\sqrt{12}\)
\(=\frac{2}{3}\sqrt{3}-\frac{1}{4}\sqrt{2\times3^2}+\frac{2}{5}\sqrt{2}-\frac{1}{4}\sqrt{3\times2^2}\)
\(=\frac{2}{3}\sqrt{3}-\frac{3}{4}\sqrt{2}+\frac{2}{5}\sqrt{2}-\frac{1}{2}\sqrt{3}\)
\(=\frac{1}{6}\sqrt{3}-\frac{7}{20}\sqrt{2}=\frac{10\sqrt{3}-21\sqrt{2}}{60}\)
b) \(\left(\sqrt{10}+\sqrt{2}\right)\left(6-2\sqrt{5}\right)\sqrt{3+\sqrt{5}}\)
\(=\sqrt{2}\left(\sqrt{5}+1\right)\left(5-2\sqrt{5}\times1+1\right)\sqrt{3+\sqrt{5}}\)
\(=\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)^2\sqrt{6+2\sqrt{5}}\)
\(=4\left(\sqrt{5}-1\right)\sqrt{5+2\sqrt{5}\times1+1}\)
\(=4\left(\sqrt{5}-1\right)\sqrt{\left(\sqrt{5}+1\right)^2}=4\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)\)
\(=4^2=16\)
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giải pt
\(\frac{4}{x}+\sqrt{x-\frac{1}{x}}\)= \(x+\sqrt{2x-\frac{5}{x}}\)
\(\sqrt{3x^2-7x+3}-\sqrt{x^2-2}=\sqrt{3x^2-5x-1}-\)\(\sqrt{x^2-3x+4}\)
\(\left(x+2\right)\sqrt{x+1}=2x+1\)
CỨU TÔI VỚI NGÀY MAI I HOK ÒI. PLEASE HELP HELP HELP ME
Bài 1 :
T =\(\left(\frac{\sqrt{x}+2}{3\sqrt{x}}+\frac{2}{\sqrt{x}+1}-3\right):\frac{2-4\sqrt{x}}{\sqrt{x}+1}+\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
a, Tìm ĐKXĐ
b, Rút gọn
c, Tìm x để T < 0
Help me !!!
a, ĐKXĐ: x>0 (1)
b,T= (\(\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)+6\sqrt{x}-9\sqrt{x}\left(\sqrt{x}+1\right)}{3\sqrt{x}\left(\sqrt{x}+1\right)}\)).(\(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\))+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{x+3\sqrt{x}+2+6\sqrt{x}-9x-9\sqrt{x}}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{2-8x}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{2\left(1-2\sqrt{x}\right)\left(1+2\sqrt{x}\right)}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2\left(1-2\sqrt{x}\right)}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\frac{1+2\sqrt{x}}{3\sqrt{x}}\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\) = \(\frac{x-\sqrt{x}}{3\sqrt{x}}\)=\(\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{3\sqrt{x}}\)=\(\frac{\sqrt{x}-1}{3}\)
c, Để T<0 \(\Leftrightarrow\)\(\frac{\sqrt{x}-1}{3}\) <0 \(\Leftrightarrow\) \(\sqrt{x}\)-1<0 \(\Leftrightarrow\) \(\sqrt{x}\)<1\(\Leftrightarrow\) x<1 mà do ĐK (1)
=> Để T<0 \(\Leftrightarrow\) 0<x<1
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Rút gọn biểu thức :
E=\(\frac{\sqrt{2x+2\sqrt{x^2-4}}}{\sqrt{x^2-4}+x+2}\)
F=\(\frac{\left(\frac{3}{\sqrt{1+a}}+\sqrt{1+a}\right)}{\left(\frac{3}{\sqrt{1-a^2}}+1\right)}\)
HELP ME !
Help me
Tìm điều kiện củasqrt{A}
1) sqrt{sqrt{5}-sqrt{3}x}
2) sqrt{frac{-2sqrt{6}+sqrt{23}}{-x+5}}
3) sqrt{2011-m}
4)sqrt{frac{2sqrt{15}-sqrt{59}}{x-7}}
5)sqrt{49x^2-24x+4}
6)sqrt{frac{12x+5}{sqrt{3}}}
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Tìm điều kiện của\(\sqrt{A}\)
1) \(\sqrt{\sqrt{5}-\sqrt{3}x}\)
2) \(\sqrt{\frac{-2\sqrt{6}+\sqrt{23}}{-x+5}}\)
3) \(\sqrt{2011-m}\)
4)\(\sqrt{\frac{2\sqrt{15}-\sqrt{59}}{x-7}}\)
5)\(\sqrt{49x^2-24x+4}\)
6)\(\sqrt{\frac{12x+5}{\sqrt{3}}}\)
Help meTìm điều kiện củasqrt{A}1) sqrt{sqrt{5}-sqrt{3}x}2) sqrt{frac{-2sqrt{6}+sqrt{23}}{-x+5}}3) sqrt{2011-m}4)sqrt{frac{2sqrt{15}-sqrt{59}}{x-7}}5)sqrt{49x^2-24x+4}6)sqrt{frac{12x+5}{sqrt{3}}}
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Help me
Tìm điều kiện của\(\sqrt{A}\)
1) \(\sqrt{\sqrt{5}-\sqrt{3}x}\)
2) \(\sqrt{\frac{-2\sqrt{6}+\sqrt{23}}{-x+5}}\)
3) \(\sqrt{2011-m}\)
4)\(\sqrt{\frac{2\sqrt{15}-\sqrt{59}}{x-7}}\)
5)\(\sqrt{49x^2-24x+4}\)
6)\(\sqrt{\frac{12x+5}{\sqrt{3}}}\)