A,B,D là đúng. Còn đâu là sai ( ý kiến của riêng mk)
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1/ Cho Dfrac{x^2-sqrt{x}}{x+sqrt{x}+1}-frac{x^2+sqrt{x}}{x-sqrt{x}+1}với 0≤x≤1
a) Rút gọn
b) CMinh 1-sqrt{D+x+1}sqrt{x}
2/Cho Efrac{15sqrt{x}-11}{x+2sqrt{x}-3}+frac{3sqrt{x}-2}{1-sqrt{x}}-frac{2sqrt{x}+3}{sqrt{x}+3}với x≥0 và x≠1
a) Rút gọn
b) Tìm giá trị của x để E frac{1}{2}
c) So sánh E với frac{2}{3}
3/Cho Gleft(frac{x-3sqrt{x}}{x-9}-1right):left(frac{9-x}{x+sqrt{x}-6}+frac{sqrt{x}-3}{sqrt{x}-2}-frac{sqrt{x}+2}{sqrt{x}+3}right)với x≥0,x≠4,x≠9
a) Rút gọn
b) Tìm x để G1
Đọc tiếp
1/ Cho D=\(\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}\)với 0≤x≤1
a) Rút gọn
b) CMinh 1\(-\sqrt{D+x+1}=\sqrt{x}\)
2/Cho E=\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)với x≥0 và x≠1
a) Rút gọn
b) Tìm giá trị của x để E = \(\frac{1}{2}\)
c) So sánh E với \(\frac{2}{3}\)
3/Cho G=\(\left(\frac{x-3\sqrt{x}}{x-9}-1\right):\left(\frac{9-x}{x+\sqrt{x}-6}+\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}+3}\right)\)với x≥0,x≠4,x≠9
a) Rút gọn
b) Tìm x để G<1
25 tháng 4 2020 lúc 11:56
Gpt: a) sqrt[4]{3left(x+5right)}-sqrt[4]{11-x}sqrt[4]{13+x}-sqrt[4]{3left(3-xright)}
b) frac{1+2sqrt{x}-xsqrt{x}}{3-x-sqrt{2-x}}2left(frac{1+xsqrt{x}}{1+x}right) c) sqrt{x+1}+frac{4left(sqrt{x+1}+sqrt{x-2}right)}{3left(sqrt{x-2}+1right)^2}3
d) sqrt{frac{x-2}{x+1}}+frac{x+2}{left(sqrt{x+2}+sqrt{x-2}right)^2}1 e) 2x+1+xsqrt{x^2+2}+left(x+1right)sqrt{x^2+2x+2}0
f) sqrt{2x+3}cdotsqrt[3]{x+5}x^2+x-6
Đọc tiếp
Gpt: a) \(\sqrt[4]{3\left(x+5\right)}-\sqrt[4]{11-x}=\sqrt[4]{13+x}-\sqrt[4]{3\left(3-x\right)}\)
b) \(\frac{1+2\sqrt{x}-x\sqrt{x}}{3-x-\sqrt{2-x}}=2\left(\frac{1+x\sqrt{x}}{1+x}\right)\) c) \(\sqrt{x+1}+\frac{4\left(\sqrt{x+1}+\sqrt{x-2}\right)}{3\left(\sqrt{x-2}+1\right)^2}=3\)
d) \(\sqrt{\frac{x-2}{x+1}}+\frac{x+2}{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}=1\) e) \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+2}=0\)
f) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
3. a.sqrt{left(4-sqrt{17}right)^2}
b.frac{2sqrt{3}}{2}
c frac{sqrt{6}+sqrt{14}}{text{2√3+√28}}
d.frac{x+1}{sqrt{x^2-1}}
e.frac{x^2-5}{x+sqrt{5}}
f.frac{2}{2-sqrt{3}}
g.frac{sqrt{2}+1}{sqrt{2}-1}
f.frac{xsqrt{x}-1}{sqrt{x}-1}
i.frac{3}{sqrt{20}}+frac{1}{sqrt{60}}-2sqrt{frac{1}{15}}
k.frac{3}{sqrt{5}-sqrt{2}}+frac{4}{sqrt{6}+sqrt{2}}
i.(frac{1}{sqrt{5}-sqrt{3}}+frac{1}{sqrt{5}+sqrt{3}})sqrt{5}
h.left(sqrt{20}-sqrt{45}+sqrt{5}right)sqrt{5}
l.left(5sqrt{3}+3sqrt{5}right):sqrt{15}
m.frac...
Đọc tiếp
3. a.\(\sqrt{\left(4-\sqrt{17}\right)^2}\)
b.\(\frac{2\sqrt{3}}{2}\)
c \(\frac{\sqrt{6}+\sqrt{14}}{\text{2√3+√28}}\)
d.\(\frac{x+1}{\sqrt{x^2-1}}\)
e.\(\frac{x^2-5}{x+\sqrt{5}}\)
f.\(\frac{2}{2-\sqrt{3}}\)
g.\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)
f.\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)
i.\(\frac{3}{\sqrt{20}}+\frac{1}{\sqrt{60}}-2\sqrt{\frac{1}{15}}\)
k.\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
i.(\(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\))\(\sqrt{5}\)
h.\(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
l.\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
m.\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{\frac{4}{3}}\)
n.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
d\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)Asqrt{5-sqrt{21}}+sqrt{5+sqrt{21}}
b)Bfrac{sqrt{15}-sqrt{5}}{sqrt{3}-1}+frac{5-2sqrt{5}}{2sqrt{5}-4}
c)Cleft(1+frac{11-sqrt{11}}{1-sqrt{11}}right)left(frac{11+sqrt{11}}{1+sqrt{11}}+1right)
d)Dfrac{sqrt{2}}{sqrt{2}-sqrt{3}}-frac{sqrt{2}}{sqrt{2}+sqrt{3}}
e)Efrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}}
Đọc tiếp
mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)A=\(\sqrt{5-\sqrt{21}}+\sqrt{5+\sqrt{21}}\)
b)B=\(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
c)C=\(\left(1+\frac{11-\sqrt{11}}{1-\sqrt{11}}\right)\left(\frac{11+\sqrt{11}}{1+\sqrt{11}}+1\right)\)
d)D=\(\frac{\sqrt{2}}{\sqrt{2}-\sqrt{3}}-\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}\)
e)E=\(\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
Bài 1: Tính :
Csqrt{frac{3sqrt{3}-4}{2sqrt{3}+1}}-sqrt{frac{sqrt{3}+4}{5-2sqrt{3}}}
Bfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+....+frac{1}{sqrt{99}+sqrt{100}}
Dsqrt{1+sqrt{3+sqrt{13+4sqrt{3}}}}+sqrt{1-sqrt{3-sqrt{13-4sqrt{3}}}}
Bài 2 : Cho Pleft(frac{1}{sqrt{x}-1}+frac{x-sqrt{x}+6}{x+sqrt{x}-2}right):left(frac{sqrt{x}+1}{sqrt{x}+2}+frac{x-sqrt{x}-2}{x+sqrt{x}+2}right)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để P.frac{x-1}{x^2+8x} -2
Đọc tiếp
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
Trục căn ở mẫu:
\(a)\frac{5}{\sqrt{10}}\\ b)\frac{-2}{1-\sqrt{5}}\\ c)\frac{4}{\sqrt{3}+\sqrt{2}}\\ d)\frac{1}{3-2\sqrt{2}}\\ e)\frac{6-\sqrt{6}}{1-\sqrt{6}}\\ g)\frac{3\sqrt{2}-2\sqrt{3}}{2\left(\sqrt{3}-\sqrt{2}\right)}\\ h)\frac{\sqrt{3}-3}{\sqrt{3}-1}\\ i)\frac{\sqrt{15}}{5\sqrt{3}+3\sqrt{5}}\)
1. Rút gọn Afrac{sqrt{14+6sqrt{5}}-sqrt{14-6sqrt{5}}}{sqrt{left(sqrt{5}+1right)cdotsqrt{6-2sqrt{5}}}}
2.Tính a) Bleft(sqrt[3]{2}+1right)^3cdotleft(sqrt[3]{2}-1right)^3
b)Tìm Ca^3b-ab^3 với afrac{6}{2sqrt[3]{2}-2+sqrt[3]{4}}; bfrac{2}{2sqrt[3]{2}+2+sqrt[3]{4}}
3. Giải left|x^2-x+1right|-left|x-2right|6
Đọc tiếp
1. Rút gọn \(A=\frac{\sqrt{14+6\sqrt{5}}-\sqrt{14-6\sqrt{5}}}{\sqrt{\left(\sqrt{5}+1\right)\cdot\sqrt{6-2\sqrt{5}}}}\)
2.Tính a) \(B=\left(\sqrt[3]{2}+1\right)^3\cdot\left(\sqrt[3]{2}-1\right)^3\)
b)Tìm C=\(a^3b-ab^3\) với \(a=\frac{6}{2\sqrt[3]{2}-2+\sqrt[3]{4}}\); \(b=\frac{2}{2\sqrt[3]{2}+2+\sqrt[3]{4}}\)
3. Giải \(\left|x^2-x+1\right|-\left|x-2\right|=6\)
Giải phương trình sau
a,sqrt{1+x}+sqrt{8-x}+sqrt{left(x+1right)left(8-xright)}3
b, 2left(x^2+2right)5sqrt{x^3+1}
c, x^2+x+33sqrt{x^3+1}
d, 2x^2+5x-17sqrt{x^3-1}
e, sqrt{2x+1}-sqrt{3x}x-1
f, left(sqrt{x+5}-sqrt{x-2}right)left(1+sqrt{x^2+7x+10}3right)
g, sqrt{x^2-3x+2}-sqrt{x+3}sqrt{x-2}-sqrt{x^2+2x-3}
h, sqrt{4x+1}-sqrt{3x-2}frac{3+x}{5}
Giúp nhanh nha e cảm ơn
Đọc tiếp
Giải phương trình sau
a,\(\sqrt{1+x}+\sqrt{8-x}+\sqrt{\left(x+1\right)\left(8-x\right)}=3\)
b, \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)
c, \(x^2+x+3=3\sqrt{x^3+1}\)
d, \(2x^2+5x-1=7\sqrt{x^3-1}\)
e, \(\sqrt{2x+1}-\sqrt{3x}=x-1\)
f, \(\left(\sqrt{x+5}-\sqrt{x-2}\right)\left(1+\sqrt{x^2+7x+10}=3\right)\)
g, \(\sqrt{x^2-3x+2}-\sqrt{x+3}=\sqrt{x-2}-\sqrt{x^2+2x-3}\)
h, \(\sqrt{4x+1}-\sqrt{3x-2}=\frac{3+x}{5}\)
Giúp nhanh nha e cảm ơn
2 tháng 3 2020 lúc 23:45
1. a) left{{}begin{matrix}x,y,z0xyz1end{matrix}right.. Tìm max Pfrac{1}{sqrt{x^5-x^2+3xy+6}}+frac{1}{sqrt{y^5-y^2+3yz+6}}+frac{1}{sqrt{z^5-z^2+zx+6}}
b) left{{}begin{matrix}x,y,z0xyz8end{matrix}right.. Min Pfrac{x^2}{sqrt{left(1+x^3right)left(1+y^3right)}}+frac{y^2}{sqrt{left(1+y^3right)left(1+z^3right)}}+frac{z^2}{sqrt{left(1+z^3right)left(1+x^3right)}}
c) x,y,z0. Min Psqrt{frac{x^3}{x^3+left(y+zright)^3}}+sqrt{frac{y^3}{y^3+left(z+xright)^3}}+sqrt{frac{z^3}{z^3+left(x+yright)^3}}
d) a,b,c0;...
Đọc tiếp
1. a) \(\left\{{}\begin{matrix}x,y,z>0\\xyz=1\end{matrix}\right.\). Tìm max \(P=\frac{1}{\sqrt{x^5-x^2+3xy+6}}+\frac{1}{\sqrt{y^5-y^2+3yz+6}}+\frac{1}{\sqrt{z^5-z^2+zx+6}}\)
b) \(\left\{{}\begin{matrix}x,y,z>0\\xyz=8\end{matrix}\right.\). Min \(P=\frac{x^2}{\sqrt{\left(1+x^3\right)\left(1+y^3\right)}}+\frac{y^2}{\sqrt{\left(1+y^3\right)\left(1+z^3\right)}}+\frac{z^2}{\sqrt{\left(1+z^3\right)\left(1+x^3\right)}}\)
c) \(x,y,z>0.\) Min \(P=\sqrt{\frac{x^3}{x^3+\left(y+z\right)^3}}+\sqrt{\frac{y^3}{y^3+\left(z+x\right)^3}}+\sqrt{\frac{z^3}{z^3+\left(x+y\right)^3}}\)
d) \(a,b,c>0;a^2+b^2+c^2+abc=4.Cmr:2a+b+c\le\frac{9}{2}\)
e) \(\left\{{}\begin{matrix}a,b,c>0\\a+b+c=3\end{matrix}\right.\). Cmr: \(\frac{a}{b^3+ab}+\frac{b}{c^3+bc}+\frac{c}{a^3+ca}\ge\frac{3}{2}\)
f) \(\left\{{}\begin{matrix}a,b,c>0\\ab+bc+ca+abc=4\end{matrix}\right.\) Cmr: \(\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\le3\)
g) \(\left\{{}\begin{matrix}a,b,c>0\\ab+bc+ca+abc=2\end{matrix}\right.\) Max : \(Q=\frac{a+1}{a^2+2a+2}+\frac{b+1}{b^2+2b+2}+\frac{c+1}{c^2+2c+2}\)