Violympic toán 9
Các câu hỏi tương tự
3 tháng 9 2020 lúc 16:40
Tính
\(c,\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+1}+\frac{\sqrt{x}+8}{4-\sqrt{x}}\left(x>0,x\ne16\right)\)
\(d,\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}\)
Giúp nha plsss
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)
19 tháng 9 2019 lúc 20:59
Bài 1: Tìm x
a, sqrt{4x+1} 4
b, sqrt{3-x} 2
c, sqrt{x+1} + frac{1}{2}sqrt{4x+4} 6 - frac{1}{3}sqrt{9x+9}
d, sqrt{4x^2-12x+9} - x 5
e, sqrt{16x^2+8x+1} 10
Bài 2: Tìm x,y,z
x + y + z 2sqrt{x}+ 2sqrt{y-3} + 2sqrt{z}
Bài 3: Cho x y 0
Rút gọn sqrt{x^2}+sqrt{y^2}-sqrt{x^2-2xy+y^2}
Bài 4: Tìm GTNN
a, x - 2sqrt{x} + 3
b, sqrt{x-4sqrt{y}+13}
c, sqrt{2x-4sqrt{y}+6}
d, -frac{4}{x^2+2x+5}
Bài 5: Cho A frac{3sqrt{x}+11}{sqrt{x}+2}
Tìm x ϵ Z để A nguyên
Đọc tiếp
Bài 1: Tìm x
a, \(\sqrt{4x+1}\) = 4
b, \(\sqrt{3-x}\) = 2
c, \(\sqrt{x+1}\) + \(\frac{1}{2}\sqrt{4x+4}\) = 6 - \(\frac{1}{3}\sqrt{9x+9}\)
d, \(\sqrt{4x^2-12x+9}\) - x = 5
e, \(\sqrt{16x^2+8x+1}\) = 10
Bài 2: Tìm x,y,z
x + y + z = 2\(\sqrt{x}\)+ 2\(\sqrt{y-3}\) + 2\(\sqrt{z}\)
Bài 3: Cho x < y < 0
Rút gọn \(\sqrt{x^2}+\sqrt{y^2}-\sqrt{x^2-2xy+y^2}\)
Bài 4: Tìm GTNN
a, x - 2\(\sqrt{x}\) + 3
b, \(\sqrt{x-4\sqrt{y}+13}\)
c, \(\sqrt{2x-4\sqrt{y}+6}\)
d, \(-\frac{4}{x^2+2x+5}\)
Bài 5: Cho A = \(\frac{3\sqrt{x}+11}{\sqrt{x}+2}\)
Tìm x ϵ Z để A nguyên
Tìm x thuôc Z để A thuôc Z
A = \(\frac{1}{\sqrt{x}-3}\)
B = \(\frac{\sqrt{x}+6}{\sqrt{x}-2}\)
C = \(\frac{4\sqrt{x}+1}{2\sqrt{x}-1}\)
D = \(\frac{\sqrt{x}-3}{\sqrt{x}-1}\)
Câu 1 : Cho biểu thức: A=\(\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}+\frac{2\sqrt{x}+1}{\sqrt{x}-3}+\frac{\sqrt{x}+3}{2-\sqrt{x}}\)
a, Rút gọn A
b, Tính giá trị của A khi x=7-4\(\sqrt{3}\)
c, Tìm x thuộc Z để A THUỘC z
1) \(\sqrt{28+10\sqrt{3}}-\sqrt{28-10\sqrt{3}}\)
2) \(\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}\) \(-\frac{5}{1+\sqrt{6}}\)
Cho biểu thức : \(A=\left(\frac{x-3\sqrt{x}}{x-9}-1\right):\left(\frac{9-x}{x+\sqrt{x}-6}+\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}+3}\right)\)
a, Rút gọn A
b, Tìm x để A < 1
c, Tìm \(x\in Z\) để \(A\in Z\)
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 : \(Q=\frac{a+1}{a^2+2a+2}+\frac{b+1}{b^2+2b+2}+\frac{c+1}{c^2+2c+2}\)
\(P=\left(\frac{\sqrt{x}+3}{\sqrt{x}-2}+\frac{\sqrt{x}+2}{3-\sqrt{x}}+\frac{\sqrt{x}+2}{x-5\sqrt{x}+6}\right):\left(1-\frac{\sqrt{x}+1}{x+2\sqrt{x}+1}\right)\)
a) Rút gọn
b) Tìm x thuộc Z để P<0