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=>x+3 =y+5
=> x -y =5-3
x-y =2 ( do mạng lag = thóat ra)
b) => 6x -7 =0 => x = 7/6
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1)\(A=\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)....\left(\frac{1}{2008}-1\right).\left(\frac{1}{2009}-1\right)=\left(-\frac{1}{2}\right)\left(-\frac{2}{3}\right)...\left(-\frac{2008}{2009}\right)=\frac{1.2.3...2008}{2.3.4....2009}=\frac{1}{2009}\)
2)\(A=\frac{x-7}{2}\)
Do 2>0 =>A>0 <=>x-7>0<=>x>7
Vậy x>7 thì A>0
3)\(A=\frac{x+3}{x-5}\)
Do x+3>x-5 =>A<0<=>x+3>0 và x-5<0
<=>-3<x<5
Vậy -3<x<5 thì A<0
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Ta có: \(\frac{x+1}{7}=0\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
Ta có: \(\frac{3x+3}{5}=0\)
\(\Leftrightarrow3x+3=0\)
\(\Leftrightarrow3x=-3\)
\(\Leftrightarrow x=-1\)
Ta có: \(\frac{2x\left(x+1\right)}{3x+4}=0\Leftrightarrow2x\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}\)
Vậy x \(\in\left\{-1;0\right\}\) thì \(\frac{2x\left(x+1\right)}{3x+4}=0\)
Ta có: \(\frac{2x\left(x-5\right)}{x-7}=0\Leftrightarrow2x\left(x-5\right)=0\)
\(\Leftrightarrow x\left(x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}\)
Vậy \(x\in\left\{0;5\right\}\) thì \(\frac{2x\left(x-5\right)}{x-7}=0\)
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a) Dễ thấy \(x^2\)luôn dương vậy để A dương thì \(4x\ge0\)
\(\Leftrightarrow x\ge0\)
b) \(B=\left(x-3\right)\left(x+7\right)\)dương khi :
TH1: \(\hept{\begin{cases}x-3>0\\x+7>0\end{cases}\Rightarrow\hept{\begin{cases}x>3\\x>-7\end{cases}\Rightarrow}x>3}\)
TH2: \(\hept{\begin{cases}x-3< 0\\x+7< 0\end{cases}\Rightarrow\hept{\begin{cases}x< 3\\x< -7\end{cases}\Rightarrow}x< -7}\)
c) Tương tự câu b)
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a) Ta có ; \(x^2\ge0\forall x\in R\)
Nên A dương khi 4x \(\ge0\forall x\in R\)
=> \(x\ge0\)
Vậy A dương khi \(x\ge0\)
\(\left(\frac{2}{7}\right)^{x-7}=1\)
=>x-7=0
=>x=7
Vậy x=7
<=>\(\left(\frac{2}{7}\right)^{6x-7}=\left(\frac{2}{7}\right)^0\)
=> 6x-7=0=>x=7/6