Tìm x , biết : 2 mũ x / 2 mũ 2012 = 1024 ( x lớn hơn hoặc bằng 2012 )
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\(\left(x+\frac{2}{3}\right)^{2012}+\left|y-\frac{1}{4}\right|^{2000}+\left(x-y-z\right)^{2014}=0\)
\(\Leftrightarrow\hept{\begin{cases}x+\frac{2}{3}=0\\y-\frac{1}{4}=0\\x-y-z=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-\frac{2}{3}\\y=\frac{1}{4}\\z=-\frac{11}{12}\end{cases}}\).
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(x-5)^2018>=0
y+1)^2018>=0
=>(x-5)^2018+(y+1)^2018>=0
dấu = xảy ra <=>x=5;y=-1
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64 . 4x = 168
<=> 43. 4x = 416
=> 3 + x = 16
<=> x = 13
Vậy x = 13
2x.162 = 1024
<=> 2x. 28 = 210
=> x + 8 = 10
<=> x = 2
Vậy x = 2
b: Ta có: \(2^x\cdot16^2=1024\)
\(\Leftrightarrow2^x\cdot2^8=2^{10}\)
\(\Leftrightarrow x+8=10\)
hay x=2
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\(\frac{1}{1+x^2}+\frac{1}{1+y^2}\ge\frac{2}{1+xy}\) ( 1 )
\(\Leftrightarrow\left(\frac{1}{1+x^2}-\frac{1}{1+xy}\right)+\left(\frac{1}{1+y^2}-\frac{1}{1+xy}\right)\ge0\)
\(\Leftrightarrow\frac{x\left(y-x\right)}{\left(1+x^2\right)\left(1+xy\right)}+\frac{y\left(x-y\right)}{\left(1+xy^2\right)\left(1+xy\right)}\ge0\)
\(\Leftrightarrow\frac{\left(y-x\right)^2\left(xy-1\right)}{\left(1+x^2\right)\left(1+y^2\right)\left(1+xy\right)}\ge0\) ( 2 )
\(\Rightarrow\)Bất đẳng thức ( 2 ) \(\Rightarrow\) Bất đẳng thức ( 1 )
( Dấu " = " xảy ra khi x = y )
Chúc bạn học tốt !!!
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|x - 2011| \(\ge\) 2012
\(\Rightarrow\orbr{\begin{cases}x-2011\ge2012\\x-2011\ge-2012\end{cases}\Rightarrow\orbr{\begin{cases}x\ge4023\\x\ge-1\end{cases}}}\)
Vậy x \(\ge\) -1
Ta có
\(\left|x-2011\right|\ge2012\Rightarrow\orbr{\begin{cases}x-2011\ge2012\\x-2011\le2012\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-2011\ge2012\\2011-x\ge2012\end{cases}\Rightarrow\orbr{\begin{cases}x\ge4023\\-x\ge1\end{cases}}}\orbr{\begin{cases}x\ge4023\\x\le-1\end{cases}}\)
Vậy \(x\ge4023\)hoặc \(x\le-1\)
Lưu ý \(-x>1\Rightarrow x< -1\)
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3^x + 3^x-2 = 810.
3^x + 3^x.3^2 = 810
3^x . (1 + 3^2) = 810
3^x . 10 = 810
3^x = 81
3^x = 3^4
=> x = 4
Vậy x = 4 Xin 1 tích nha ahehe:)))
Có: \(\dfrac{2^x}{2^{2012}}=1024\)
\(\Rightarrow\dfrac{2^x}{2^{2012}}=2^{10}\Rightarrow2^x=2^{10}\cdot2^{2012}=2^{2022}\)
\(\Rightarrow x=2022\)
\(\dfrac{2^x}{2^{2012}}=1024\)
\(\Rightarrow2^x=2^{10}.2^{2012}=2^{2022}\)
Vì \(2\ne\pm1;2\ne0\) nên \(x=2022\)
Vậy...........
Chúc bạn học tốt!!!