a)Tìm số nguyên x, biết: 2016 : [25 – (3x + 2)] = 32.7
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biến đổi nhá (x-2015+1)(x-2015-1)<0......\(y=\left(x-2015\right)^2-1\le0\)giải tiếp thôi
\(\dfrac{-19}{23}< \dfrac{7}{x}< \dfrac{-19}{25}\\ \Leftrightarrow7:\dfrac{-19}{23}< x< 7:\dfrac{-19}{25}\\ \Leftrightarrow\dfrac{-161}{19}< x< \dfrac{-175}{19}\\ \Leftrightarrow-161< 19x< -175\\ \Leftrightarrow x=-9\)
Ta có: \(2016:\left[25-\left(3x+2\right)\right]=32\cdot7\)
\(\Leftrightarrow25-\left(3x+2\right)=9\)
\(\Leftrightarrow3x+2=16\)
\(\Leftrightarrow3x=14\)
hay \(x=\dfrac{14}{3}\)
2016 : [25 - (3x+2)]=32.7
25 - (3x+2)= 2016 : 224
25 - (3x+2)= 9
3x+2 = 16
3x=14
x=\(\dfrac{14}{3}\)
\(P=\sqrt{\frac{1}{36}\left(11a+7b\right)^2+\frac{59\left(a-b\right)^2}{36}}+\sqrt{\frac{1}{36}\left(7a+11b\right)+\frac{59\left(a-b\right)^2}{36}}\)
\(=\sqrt{\frac{1}{16}\left(3a+5b\right)^2+\frac{5\left(a-b\right)^2}{16}}+\sqrt{\frac{1}{16}\left(5a+3b\right)^2+\frac{5\left(a-b\right)^2}{16}}\)
\(\ge\frac{1}{6}\left(11a+7b\right)+\frac{1}{6}\left(7a+11b\right)+\frac{1}{4}\left(3a+5b\right)+\frac{1}{4}\left(5a+3b\right)\)
\(=5\left(a+b\right)=5.2016=10080\)
Ta có: \(\hept{\begin{cases}\left(2x-y-4\right)^{2016}\ge0\\\left(3x+2y-13\right)^{2016}\ge0\end{cases}}\)
\(\Rightarrow\left(2x-y-4\right)^{2016}+\left(3x+2y-13\right)^{2016}\ge0\)
Dấu bằng xảy ra khi
\(\hept{\begin{cases}2x-y-4=0\\3x+2y-13=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3\\y=2\end{cases}}\)
\(\Rightarrow A=\left(x-y\right)^{2016}+2016=\left(3-2\right)^{2016}+2016=2017\)
\(2016:\left[25-\left(3x+2\right)\right]=32\cdot7\\ \Rightarrow2016:\left[25-\left(3x+2\right)\right]=224\\ \Rightarrow25-3x-2=2016:224\\ \Rightarrow23-3x=9\\ \Rightarrow3x=23-9\\ \Rightarrow3x=14\\ \Rightarrow x=\dfrac{14}{3}\)
2016 : [25-(3x+2)]=32.7
25-(3x+2)= 2016:32.7
25-(3x+2)= 61.7
3x+2= 25-61.7
3x+2= -36.7
3x= -36.7-2
3x= -38.7
x=-38.7:3
x= -12.9