(7,5x(-3.5)-2.5x3,5)x1,9:(-17,5)
Làm chi tiết nha
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\(\left[7.5\cdot\left(-3.5\right)-2.5\cdot3.5\right]\cdot1.9:\left(-17.5\right)\)
\(=-3.5\cdot10\cdot\dfrac{1.9}{-17.5}\)
\(=\dfrac{35\cdot1.9}{17.5}=2\cdot1.9=3.8\)
\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.\left(3+2.6+7.21\right)}{5.\left(3+2.6+7.21\right)}=\frac{2}{5}\)
\(M=x^4-4x+7=\left(x^2-4x+4\right)+3=\left(x-2\right)^2+3\ge3\)
\(minM=3\Leftrightarrow x=2\)
\(P=x^2-6x+y^2-2y+12=\left(x^2-6x+9\right)+\left(y^2-2y+1\right)+2=\left(x-3\right)^2+\left(y-1\right)^2+2\ge2\)
\(minP=2\Leftrightarrow\)\(\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
c.
\(\Leftrightarrow\left\{{}\begin{matrix}2x+1>0\\\left(2x+1\right)^2>\left(x+2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{1}{2}\\x^2>1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{1}{2}\\\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow x>1\)
d.
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\2-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}2-x\ge0\\x>\left(2-x\right)^2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2\\x^2-5x+4< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>2\\\left\{{}\begin{matrix}x\le2\\1< x< 4\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x>2\\1< x\le2\end{matrix}\right.\)
\(\Leftrightarrow x>1\)
2.
Do \(a\in\left(\dfrac{\pi}{2};\pi\right)\Rightarrow sina>0\)
\(\Rightarrow sina=\sqrt{1-cos^2a}=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}=\dfrac{4}{5}\)
\(\dfrac{\left[7.5\cdot\left(-3.5\right)-2.5\cdot3.5\right]\cdot1.9}{-17.5}\)
\(=\dfrac{-3.5\left(7.5+2.5\right)\cdot1.9}{-17.5}\)
\(=\dfrac{35\cdot1.9}{17.5}=2\cdot1.9=3.8\)