Tìm x, y \(\in\)Z. Sao cho xy + 2x - y = 5
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\(a,\left(a+2\right)^2+\left|3b-4\right|=0\)
\(\Rightarrow\hept{\begin{cases}\left(a+2\right)^2=0\\\left|3b-4\right|=0\end{cases}}\Rightarrow\hept{\begin{cases}a+2=0\\3b-4=0\end{cases}}\Rightarrow\hept{\begin{cases}a=-2\\b=\frac{4}{3}\end{cases}}\)
\(b,\left(3a^2+27\right)^2+\left|b-1\right|=0\)
\(\Rightarrow\hept{\begin{cases}\left(3a^2+27\right)^2=0\\\left|b-1\right|=0\end{cases}\Rightarrow\hept{\begin{cases}3a^2+27=0\\b-1=0\end{cases}}}\)
\(\Rightarrow\hept{\begin{cases}3a^2=27\\b=1\end{cases}\Rightarrow\hept{\begin{cases}a^2=9\\b=1\end{cases}\Rightarrow}\hept{\begin{cases}\orbr{\begin{cases}a=3\\a=-3\end{cases}}\\b=1\end{cases}}}\)
\(\Rightarrow\hept{\begin{cases}3a^2=27\\b=1\end{cases}\Rightarrow\hept{\begin{cases}a^2=9\\b=1\end{cases}\Rightarrow}\hept{\begin{cases}\orbr{\begin{cases}a=3\\a=-3\end{cases}}\\b=1\end{cases}}}\)
\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.6^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{2^{29}.3^{18}.\left(5.2.1-9\right)}{2^{28}.3^{18}.\left(5.1.3-7.2.1\right)}\)
\(A=\frac{2.1}{1}=2\)
Bài :1
\(Q=\frac{2010+2011+2012}{2011+2012+2013}\)
\(Q=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow P>Q\)
\(x^2=5\Leftrightarrow\orbr{\begin{cases}x=\sqrt{5}\\x=-\sqrt{5}\end{cases}}\)
\(x^3-2x=0\Leftrightarrow x\left(x^2-2\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^2=2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\\orbr{\begin{cases}x=\sqrt{2}\\x=-\sqrt{2}\end{cases}}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=+-\sqrt{2}\end{cases}}\)