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vì (x-2007)2 >= 0 với mọi x
(y + 3/4)2 >= 0 với mọi y
=> (x-2007)2 + (y + 3/4)2 =0
<=> x=2007 và y=-3/4
Do (x-2007)^2 >= 0 ; (y + 3/4)^2 >= 0
=> (x-2007)^2 + (y + 3/4)^2 = 0
<=>(x-2007)^2 = 0 => x-2007 =0 => x=2007
(y-3/4)^4 = 0 => x-3/4 = 0 => x=3/4
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\(\left(3x-7\right)^{2009}=\left(3x-7\right)^{2007}\)
\(\Leftrightarrow\left(3x-7\right)^{2009}-\left(3x-7\right)^{2007}=0\)
\(\left(3x-7\right)^{2007}.\left[\left(3x-7\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(3x-7\right)^{2007}=0\\\left(3x-7\right)^2=1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{3}\\\left(3x-7\right)=\pm1\end{cases}}}\)
=> \(x=\frac{7}{3},x=2,x=\frac{8}{3}\)
Vậy ...
2/\(\frac{5^{102}.9^{1009}}{3^{2018}.25^{50}}=\frac{5^{100+2}.3^{2.1009}}{3^{2018}.5^{2.50}}=\frac{5^{100}.5^2.3^{2018}}{3^{2018}.5^{100}}=5^2=25\)
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(3x - 7)2007 = (3x - 7)2005
=> (3x - 7)2007 - (3x - 7)2005 = 0
=> (3x - 7)2005 [(3x - 7)2 - 1] = 0
=> (3x - 7)2005 = 0 hoặc (3x - 7)2 - 1 = 0
+) (3x - 7)2005 = 0
=> 3x - 7 = 0
=> 3x = 7
=> x = 7/3
+) (3x - 7)2 - 1 = 0
=> (3x - 7)2 = 1
=> 3x - 7 = 1 => 3x = 8 => x = 8/3
3x - 7 = -1 => 3x = 6 => x = 2
Vậy: x \(\in\){-7/3;8/3;2
(-2)x - 1 + 2007 = 2263
=> (-2)x - 1 = 256
=> (-2)x - 1 = (-2)8
=> x - 1 = 8
=> x = 9
vậy_
\(\left(-2\right)^{x-1}+2007=2263\)
\(\left(-2\right)^{x-1}=2263-2007\)
\(\left(-2\right)^{x-1}=256\)
\(\left(-2\right)^{x-1}=\left(-2\right)^8\)
\(\Rightarrow x-1=8\Rightarrow x=8+1\)
\(\Rightarrow x=9\)