\(f\left(x\right)=x^3-3x^2+3x+3=\left(x-1\right)^3+2\)
Thay vào là OK!!
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Giải các bất phương trình sau :
a) 4x-8ge3left(3x-1right)-2x+1
b) left(x-3right)left(x+2right)+left(x+4right)^2le2xleft(x+5right)+4
c) 3x-dfrac{x+2}{3}ledfrac{3left(x-2right)}{2}+5-x
d) x-dfrac{x+2}{3}ge3x-1+dfrac{x}{2}
e) dfrac{xleft(x+2right)}{3}+dfrac{left(x-1right)left(x+2right)}{2}gedfrac{5left(x+1right)^2}{6}+1
f) dfrac{x+5}{2012}+dfrac{x+6}{2011}+dfrac{x+7}{2010}-3
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Giải các bất phương trình sau :
a) \(4x-8\ge3\left(3x-1\right)-2x+1\)
b) \(\left(x-3\right)\left(x+2\right)+\left(x+4\right)^2\le2x\left(x+5\right)+4\)
c) \(3x-\dfrac{x+2}{3}\le\dfrac{3\left(x-2\right)}{2}+5-x\)
d) \(x-\dfrac{x+2}{3}\ge3x-1+\dfrac{x}{2}\)
e) \(\dfrac{x\left(x+2\right)}{3}+\dfrac{\left(x-1\right)\left(x+2\right)}{2}\ge\dfrac{5\left(x+1\right)^2}{6}+1\)
f) \(\dfrac{x+5}{2012}+\dfrac{x+6}{2011}+\dfrac{x+7}{2010}>-3\)
Thực hiện phép tínha,left(dfrac{1}{x^2+x}-dfrac{2-x}{x+1}right):left(dfrac{1}{x}+x-2right)b,left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}c,left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)d,dfrac{x+1}{x+2}:left(dfrac{x+2}{x+3}:dfrac{x+3}{x+1}right)e,dfrac{8}{left(x^2+3right)left(x^2-1right)}+dfrac{2}{x^2+3}+dfrac{1}{x+1}f,dfrac{x+y}{2left(x-yright)}-dfrac{x-y}{2left(x+yright)}+dfrac{2y^2}{x^2-y^2}g,dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+d...
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Thực hiện phép tính
\(a,\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(b,\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(c,\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
\(d,\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
\(e,\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
\(f,\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
\(g,\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
\(h,\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
a x^2-x0 b x^2-2x0 c (x+1)(x+2)(2-x)(x+2)
d dfrac{1}{x-2}+3dfrac{3-x}{x-2} đ dfrac{8-x}{x-7}-8dfrac{1}{x-7}
e dfrac{x}{2left(x-3right)}+dfrac{x}{2left(x+1right)}dfrac{2x}{left(x+1right)left(x-3right)}
f 5+dfrac{76}{x^2-16}dfrac{2x-1}{x+4}-dfrac{3x-1}{4-x}
g dfrac{90}{x}-dfrac{36}{x-6}2 h dfrac{1}{x}+dfrac{1}{x+10}dfrac{1}{12} i dfrac{x+3}{x-3}-dfrac{1}{...
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a \(x^2-x=0\) b \(x^2-2x=0\) c (x+1)(x+2)=(2-x)(x+2)
d \(\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\) đ \(\dfrac{8-x}{x-7}-8=\dfrac{1}{x-7}\)
e \(\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x+1\right)}=\dfrac{2x}{\left(x+1\right)\left(x-3\right)}\)
f \(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)
g \(\dfrac{90}{x}-\dfrac{36}{x-6}=2\) h \(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\) i \(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)
k \(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\) l \(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)
m\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
n \(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\) j \(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)
q \(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
Cần gấp ạ
Giải phương trình sau: \(\left(2x^2+x-2013\right)^2+4\left(x^2-5x-2012\right)^2=4\left(2x^2+x-2013\right)\left(x^2-5x-2012\right)\)
Giải phương trình sau:
\(\left(2x^2+x-2013\right)^2+4\left(x^2-5x-2012\right)^2=4\left(2x^2+x-2013\right)\left(x^2-5x-2012\right)\)
Cmr:
1, \(f\left(x\right)=25x^2-20x+\dfrac{9}{2}>0\)
2, \(f\left(x\right)=4x^2-28x+50>0\)
3, \(f\left(x\right)=-16x^2+72x-82< 0\)
4, \(f\left(x\right)=9x^2+66x-122< 0\)
5, \(f\left(x;y\right)=4x^2+9y^2-12x+6y+11>0\)
6, \(f\left(x;y\right)=13x^2+y^2+4xy-34x-2y+27>0\)
Giải các phương trình sau :
a)\(\dfrac{5x+2}{6}\)\(-\dfrac{8x-1}{3}=\dfrac{4x+2}{5}-5\)
b)\(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
c)\(2x^3 +6x^2=x^2+3x\)
d)\(\left|x-4\right|+3x=5\)
Giải các phương trình sau:
a.\(\dfrac{5x-2}{2-2x}\)+\(\dfrac{2x-1}{2}\)=1-\(\dfrac{x^2+x-3}{1-x}\)
b.\(\dfrac{5-2x}{3}\)+\(\dfrac{\left(x+1\right)\left(x-1\right)}{3x-1}\)=\(\dfrac{\left(x+2\right)\left(1-3x\right)}{9x-3}\)
\(A=\left[\left(\dfrac{1}{x}+1\right)\cdot\dfrac{2}{x^3+3x^2+3x+1}+\dfrac{1}{1+2x+x^2}\cdot\left(1+\dfrac{1}{x^2}\right)\right]:\dfrac{x-1}{x^3}\)
a) Rút gọn
b) x bằng mấy để A = 3?
c) x thuộc Z, x bằng mấy để A thuộc Z?