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\(a,\left(x+1\right)^2=81\)
\(\left(x+1\right)^2=9^2\) Hoặc \(\left(x+1\right)^2=\left(-9\right)^2\)
\(\left(x+1\right)=9\) \(x+1=-9\)
\(x=8\) \(x=-10\)
b,\(\left(x+5\right)^{^{ }3}=-64\)
\(\left(x+5\right)^3=\left(-4\right)^3\)
\(x+5=-4\)
=> \(x=-9\)
c,\(\left(2x-3\right)^2=9\)
=>\(\left(2x-3\right)^2=3^2\)Hoặc \(\left(2x-3\right)^2=\left(-3\right)^2\)
\(2x-3=3\) \(2x-3=-3\)
\(2x=6\) \(2x=0\)
=> \(\hept{\begin{cases}x=3\\x=0\end{cases}}\)
d, \(\left(4x+1\right)^3=27\)
\(\left(4x+1\right)^{^{ }3}=3^3\)
\(4x+1=3\)
\(4x=2\)
\(x=\frac{1}{2}\)
\(D=\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{8^6}{4}=\frac{\left(2^3\right)^6}{2^2}=\frac{2^{18}}{2^2}=2^{16}\)
\(D=\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{4^{15}+4^{10}}{4^6+4^{11}}=\frac{4^{10}.4^5+4^{10}}{4^6+4^6.4^5}=\frac{4^{10}.\left(4^5+1\right)}{4^6.\left(4^5+1\right)}=\frac{4^{10}}{4^6}=4^4=256\)
phần D trên mk làm sai xin lỗi nha
a. \(\left(x+5\right)^3=-64\)
\(\left(x+5\right)^3=\left(-4\right)^3\)
\(\Rightarrow x+5=-4\)
=> x = -9
b. \(|2x-5|=8\)
\(\left[{}\begin{matrix}2x-5=8\\2x-5=-8\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=13\\2x=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{2}\\x=\dfrac{-3}{2}\end{matrix}\right.\)
c. \(\left|\dfrac{3}{4}x-\dfrac{1}{5}\right|=2\)
\(\left[{}\begin{matrix}\dfrac{3}{4}x-\dfrac{1}{5}=2\\\dfrac{3}{4}x-\dfrac{1}{5}=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\dfrac{3}{4}x=\dfrac{11}{5}\\\dfrac{3}{4}x=\dfrac{-9}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{44}{15}\\x=\dfrac{-12}{5}\end{matrix}\right.\)
d. \(\left|3x-6\right|=x+4\)
\(\left[{}\begin{matrix}3x-6=x+4\\3x-6=-x-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x-x=4+6\\3x+x=-4+6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=10\\4x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{1}{2}\end{matrix}\right.\)
e. \(\left|x-3\right|=2x+1\)
\(\left[{}\begin{matrix}x-3=2x+1\\x-3=-2x-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-2x=1+3\\x+2x=-1+3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}-x=4\\3x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{2}{3}\end{matrix}\right.\)
a) \(\left(x-5\right)\left(x+8\right)-\left(x+4\right)\left(x-1\right)\)
\(=\left(x^2+3x-40\right)-\left(x^2+3x-4\right)\)
\(=x^2+3x-40-x^2-3x+4\)
\(=-36\)
b)\(x^4\left(x^2-1\right)\left(x^2+1\right)\)
\(=x^4\left(x^4-1\right)\)
\(=x^8-x^4\)
a) ( x + 5 )3 = -64
x + 5 = - 4
x = - 4 - 5
x = -9
b) (2x - 3)2=9
2x - 3 = 3
2x = 3+3
2x = 6
x = 6 : 2
x = 3
e) \(\dfrac{8}{2x}=4\)
=> 4 . 2x = 8
8x =8
x = 8 : 8
x = 1
g) \(\left(\dfrac{1}{2}\right)^{2x-1}=\dfrac{1}{8}\)
\(\left(\dfrac{1}{2}\right)^{2x}:\left(\dfrac{1}{2}\right)^1=\dfrac{1}{8}\)
\(\left(\dfrac{1}{2}\right)^{2x}:\dfrac{1}{2}=\dfrac{1}{8}\)
\(\left(\dfrac{1}{2}\right)^{2x}=\dfrac{1}{8}.\dfrac{1}{2}\)
\(\left(\dfrac{1}{2}\right)^{2x}=\dfrac{1}{16}\)
\(\left(\dfrac{1}{2}\right)^{2x}=\left(\dfrac{1}{2}\right)^{2.2}\)
=> x = 2
h) \(\left(\dfrac{1}{2}\right)^2.x=\left(\dfrac{1}{2}\right)^5\)
\(\dfrac{1}{4}.x=\dfrac{1}{32}\)
x = \(\dfrac{1}{32}:\dfrac{1}{4}\)
x = \(\dfrac{1}{8}\)
i) \(\left(\dfrac{-1}{3}\right)x=\dfrac{1}{81}\)
\(x=\dfrac{1}{81}:\left(\dfrac{-1}{3}\right)\)
\(x=\dfrac{-1}{27}\)
a) (x + 5)3 = -64
=> (x + 5)3 = (-4)3
x + 5 = -4
x = -4 - 5
x = -9
b) (2x - 3)2 = 9
=> (2x - 3)2 = (\(\pm\)3)2
=> 2x - 3 = 3 hoặc 2x - 3 = -3
*2x - 3 = 3
2x = 3 + 3
2x = 9
x = \(\dfrac{9}{2}\)
*2x - 3 = -3
2x = -3 + 3
2x = 0
x = 0 : 2
x = 0
Vậy x \(\in\left\{\dfrac{9}{2};0\right\}\)
c) \(\dfrac{x}{\dfrac{4}{2}}=\dfrac{4}{\dfrac{x}{2}}\)
=> \(x.\dfrac{x}{2}=4.\dfrac{4}{2}\)
\(\dfrac{x}{2}=8\)
x = 8 : 2
x = 4
d) \(\dfrac{-32}{\left(-2\right)^n}=4\)
\(\Rightarrow\dfrac{\left(-2\right)^5}{\left(-2\right)^n}=\left(-2\right)^2\)
=> (-2)n . (-2)2= (-2)5
(-2)n = (-2)5 : (-2)2
(-2)n = (-2)3
Vậy n = 3
e) \(\dfrac{8}{2x}=4\)
=> 2x . 4 = 8
2x = 8 : 4
2x = 2
x = 1
g) \(\left(\dfrac{1}{2}\right)^{2x-1}=\dfrac{1}{8}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^3\)
2x - 1 = 3
2x = 3 + 1
2x = 4
x = 4 : 2
x = 2
h) \(\left(\dfrac{1}{2}\right)^2.x=\left(\dfrac{1}{2}\right)^5\)
\(x=\left(\dfrac{1}{2}\right)^5:\left(\dfrac{1}{2}\right)^2\)
\(x=\left(\dfrac{1}{2}\right)^3\)
\(x=\dfrac{1}{8}\)
i) \(\left(\dfrac{-1}{3}\right)x=\dfrac{1}{81}\)
\(x=\dfrac{1}{81}:\left(\dfrac{-1}{3}\right)\)
\(x=\left(\dfrac{-1}{3}\right)^4:\left(\dfrac{-1}{3}\right)\)
\(x=\left(\dfrac{-1}{3}\right)^3\)
\(x=\dfrac{-1}{27}\).
1: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^6\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{18}\)
=>4x=18
hay x=9/2
2: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^{36}\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{108}\)
=>4x=108
hay x=27
3: \(\left(\dfrac{1}{81}\right)^x=\left(\dfrac{1}{27}\right)^4\)
\(\Leftrightarrow\left(\dfrac{1}{3}\right)^{4x}=\left(\dfrac{1}{3}\right)^{12}\)
=>4x=12
hay x=3
\(A=3\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)...\left(x^{64}+1\right)\)
\(\Leftrightarrow A=\frac{3\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^8-1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{16}-1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{32}-1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{64}-1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{128}-1\right)}{x^2-1}\)