Violympic toán 9
Các câu hỏi tương tự
Cho \(x=\sqrt[3]{2020}\)
Tính \(A=\sqrt[3]{\frac{x^3-3x+\left(x^2-1\right)\sqrt{x^2-4}}{2}}+\sqrt[3]{\frac{x^3-3x-\left(x^2-1\right)\sqrt{x^2-4}}{2}}\)
Giair phương trình
a, \(3\sqrt{\left(x+1\right)\left(x-3\right)}+x^2-2x=7\)
b, \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
c, \(\left(x^2-4\right)+4\left(x-2\right).\sqrt{\frac{x+2}{x-2}}=3\)
d, \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}=1\)
e, \(3\sqrt{2+x}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
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) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
a)sqrt{1-x}left(x-3x^2right)x^3-3x^2+2x+6
b)x^2+x+12sqrt{x+1}36
c)3x-1+frac{x-1}{4x}sqrt{3x+1}
d)sqrt{x^2+12}-3xsqrt{x^2+5}-5
e)4x^2+12+sqrt{x-1}4left(xsqrt{5x-1}+sqrt{9-5x}right)
f)4x^3-25x^2+43x+xsqrt{3x-2}22+sqrt{3x-2}
g)2left(x+1right)sqrt{x}+sqrt{3left(2x^3+5x^2+4x+1right)}5x^3-3x^2+8
h)sqrt{x^2+12}-sqrt{x^2+5}3x-5
i)sqrt{1-3x}-sqrt[3]{3x-1}left|6x-2right|
k)sqrt{2x^3+3x^2-1}2x^2+2x-x^3-1
l)sqrt{x^2+x-2}+x^2sqrt{2left(x-1right)}+1
Đọc tiếp
a)\(\sqrt{1-x}\left(x-3x^2\right)=x^3-3x^2+2x+6\)
b)\(x^2+x+12\sqrt{x+1}=36\)
c)\(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)
d)\(\sqrt{x^2+12}-3x=\sqrt{x^2+5}-5\)
e)\(4x^2+12+\sqrt{x-1}=4\left(x\sqrt{5x-1}+\sqrt{9-5x}\right)\)
f)\(4x^3-25x^2+43x+x\sqrt{3x-2}=22+\sqrt{3x-2}\)
g)\(2\left(x+1\right)\sqrt{x}+\sqrt{3\left(2x^3+5x^2+4x+1\right)}=5x^3-3x^2+8\)
h)\(\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\)
i)\(\sqrt{1-3x}-\sqrt[3]{3x-1}=\left|6x-2\right|\)
k)\(\sqrt{2x^3+3x^2-1}=2x^2+2x-x^3-1\)
l)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)
28 tháng 11 2019 lúc 23:30
Giải các pt sau:
a) sqrt{x+8}+frac{9x}{sqrt{x+8}}-6sqrt{x}0
b) x^4-2x^3+sqrt{2x^3+x^2+2}-20
c) 3xsqrt[3]{x+7}left(x+sqrt[3]{x+7}right)7x^3+12x^2+5x-6
d) 4x^2+left(8x-4right)sqrt{x}-13x+2sqrt{2x^2+5x-3}
e) 16x^2+19x+7+4sqrt{-3x^2+5x+2}left(8x+2right)left(sqrt{2-x}+2sqrt{3x+1}right)
f) left(5x+8right)sqrt{2x-1}+7xsqrt{x+3}9x+8-left(x+26right)sqrt{x-1}
g) sqrt[3]{3x+1}+sqrt[3]{5-x}+sqrt[3]{2x-9}-sqrt[3]{4x-3}0
Đọc tiếp
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
Giải hệ phương trình :
1, left{{}begin{matrix}x-2y12x-y4end{matrix}right.
2, left{{}begin{matrix}frac{x}{y}-frac{y}{y+12}1frac{x}{y+12}-frac{x}{y}2end{matrix}right.
3, left{{}begin{matrix}3x^2+y^25x^2-3y1end{matrix}right.
4, left{{}begin{matrix}sqrt{3x-1}-sqrt{2y+1}12sqrt{3x-1}+3sqrt{2y+1}12end{matrix}right.
Đọc tiếp
Giải hệ phương trình :
1, \(\left\{{}\begin{matrix}x-2y=1\\2x-y=4\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\frac{x}{y}-\frac{y}{y+12}=1\\\frac{x}{y+12}-\frac{x}{y}=2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}3x^2+y^2=5\\x^2-3y=1\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}\sqrt{3x-1}-\sqrt{2y+1}=1\\2\sqrt{3x-1}+3\sqrt{2y+1}=12\end{matrix}\right.\)
1. Cho pt: x2 -2(m+1)x+m20 (1). Tìm m để pt có 2 nghiệm x1 ; x2 thỏa mãn (x1-m)2 + x2m+2.
2. Giai pt: left(x-1right)sqrt{2left(x^2+4right)}x^2-x-2
3. Giai hệ pt: left{{}begin{matrix}frac{1}{sqrt[]{x}}-frac{sqrt{x}}{y}x^2+xy-2y^2left(1right)left(sqrt{x+3}-sqrt{y}right)left(1+sqrt{x^2+3x}right)3left(2right)end{matrix}right.
4. Giai pt trên tập số nguyên x^{2015}sqrt{yleft(y+1right)left(y+2right)left(y+3right)}+1
Đọc tiếp
1. Cho pt: x2 -2(m+1)x+m2=0 (1). Tìm m để pt có 2 nghiệm x1 ; x2 thỏa mãn (x1-m)2 + x2=m+2.
2. Giai pt: \(\left(x-1\right)\sqrt{2\left(x^2+4\right)}=x^2-x-2\)
3. Giai hệ pt: \(\left\{{}\begin{matrix}\frac{1}{\sqrt[]{x}}-\frac{\sqrt{x}}{y}=x^2+xy-2y^2\left(1\right)\\\left(\sqrt{x+3}-\sqrt{y}\right)\left(1+\sqrt{x^2+3x}\right)=3\left(2\right)\end{matrix}\right.\)
4. Giai pt trên tập số nguyên \(x^{2015}=\sqrt{y\left(y+1\right)\left(y+2\right)\left(y+3\right)}+1\)
1, gpt
a,sqrt{x^2-3x+2}+sqrt{x+3}sqrt{x-2}+sqrt{x^2+2x-3}
b, left(4x+2right)sqrt{x+8}3x^2+7x+8
c,sqrt{x+sqrt{2x-1}}+sqrt{x-sqrt{2x-1}}sqrt{2}
2/ cho x,y,z thỏa mãn : left(frac{1}{x}+frac{1}{y}+frac{1}{z}right):frac{1}{x+y+z}1
tính giá trị biểu thức Bleft(x^{29}+y^{29}right)left(x^{11}+y^{11}right)left(x^{2013}+y^{2013}right)
Đọc tiếp
1, gpt
a,\(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
b, \(\left(4x+2\right)\sqrt{x+8}=3x^2+7x+8\)
c,\(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
2/ cho x,y,z thỏa mãn : \(\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right):\frac{1}{x+y+z}=1\)
tính giá trị biểu thức B=\(\left(x^{29}+y^{29}\right)\left(x^{11}+y^{11}\right)\left(x^{2013}+y^{2013}\right)\)
Cho biểu thức Pleft(frac{2sqrt{x}}{sqrt{x}+3}+frac{sqrt{x}}{sqrt{x}-3}-frac{3x+3}{x-9}right):left(frac{2sqrt{x}-2}{sqrt{x}-3}-1right)
a)Rút gọn P
b)Tìm x để P frac{1}{2}
c)Tìm x để P.left(sqrt{x}+3right)+2sqrt{x}-2+x2
d)Tìm m để P.left(sqrt{x}+3right)+xleft(sqrt{x}-mright)x-sqrt{x}left(3+mright)
Đọc tiếp
Cho biểu thức \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
a)Rút gọn P
b)Tìm x để \(P< \frac{1}{2}\)
c)Tìm x để \(P.\left(\sqrt{x}+3\right)+2\sqrt{x}-2+x=2\)
d)Tìm m để \(P.\left(\sqrt{x}+3\right)+x\left(\sqrt{x}-m\right)=x-\sqrt{x}\left(3+m\right)\)