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LT
2
25 tháng 7 2018
+) \(\left(x-3\right)^2=16\)
\(\Rightarrow\orbr{\begin{cases}\left(x-3\right)^2=4^2\\\left(x-3\right)^2=\left(-4\right)^2\end{cases}\Rightarrow}\orbr{\begin{cases}x-3=4\\x-3=-4\end{cases}}\Rightarrow\orbr{\begin{cases}x=7\\x=-1\end{cases}}\)
Vậy x = 7 hoặc x = -1
+) \(\left(1-3x\right)^3=-64\)
\(\Rightarrow\left(1-3x\right)^3=\left(-4\right)^3\)
\(\Rightarrow1-3x=-4\)
\(\Rightarrow3x=1+4\)
\(\Rightarrow3x=5\)
\(\Rightarrow x=5:3\)
\(\Rightarrow x=\frac{5}{3}\)
Vậy \(x=\frac{5}{3}\)
+) \(x^{13}=27.x^{10}\)
\(\Rightarrow x^{13}:x^{10}=27\)
\(\Rightarrow x^3=27\)
\(\Rightarrow x^3=3^3\)
\(\Rightarrow x=3\)
Vậy x = 3
+) \(\left(4x-1\right)^2=\left(1-4x\right)^4\)
\(\Rightarrow\left(4x-1\right)^2=\left(4x-1\right)^4\)
\(\Rightarrow\left(4x-1\right)^2-\left(4x-1\right)^4=0\)
\(\Rightarrow\left(4x-1\right)^2\left[1-\left(4x-1\right)^2\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(4x-1\right)^2=0\\1-\left(4x-1\right)^2=0\end{cases}}\Rightarrow\orbr{\begin{cases}\left(4x-1\right)^2=0\\\left(4x-1\right)^2=1\end{cases}}\)
TH 1 : \(\left(4x-1\right)^2=0\Rightarrow4x-1=0\Rightarrow4x=1\Rightarrow x=\frac{1}{4}\)
TH 2 : \(\left(4x-1\right)^2=1\Rightarrow\orbr{\begin{cases}4x-1=1\\4x-1=-1\end{cases}}\Rightarrow\orbr{\begin{cases}4x=2\\4x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=0\end{cases}}\)
Vậy \(x\in\left\{\frac{1}{4};\frac{1}{2};0\right\}\)
_Chúc bạn học tốt_
25 tháng 7 2018
a, (x-3)^2 = 16
=> (x-3)^2=4^2
=> x-3=4
=> x= 4+3
=> x = 7 .Vậy x =7
b,(1-3x)^3 = 64
=> ( 1-3x)^3 = 4^3
=> 1-3x = 4
=> 3x = 1-4
=> 3x = -3
=> x = -1 . Vậy x = -1
c, x^13 = 27.x^10
=> x^13 : x^10 = 27
=> x^3 = 3^3
=> x = 3 . Vậy x = 3
22 tháng 4 2020
\(2x^2-3x=2.(-1)^2-3.(-1)=2-(-3)=5\)
\(5x^2-3x-16=5.2^2-3.2-16=20-6-16=-2\)
\(5x-7y+10=5.\frac{1}{5}\)\(-7.\frac{1}{7}\)\(+10=1-1+10=10\)
\(2x-3y^2+4z^3=2.2+3.(-1)^2+4(-1)=4+3-4=3\)
Học tốt!
VT
0
23 tháng 10 2019
a) (5x+1) ^ 2 = 4^2 : 5^ 2
( 5x+1) ^2 = (4:5) ^2
=> (5x+1) = ( 4 : 5) = 0.8
5x = 0.8 - 1
x = 0.7 : 5
x = 0,14
C
0
H9
HT.Phong (9A5)
CTVHS
18 tháng 7 2023
1) \(3^x=\dfrac{9^8}{27^3\cdot81^2}\)
\(\Rightarrow3^x=\dfrac{\left(3^2\right)^8}{\left(3^3\right)^3\cdot\left(3^4\right)^2}\)
\(\Rightarrow3^x=\dfrac{3^{16}}{3^{15}}\)
\(\Rightarrow3^x=3\)
\(\Rightarrow x=1\)
2) \(\dfrac{2^{4-x}}{16^5}=32^6\)
\(\Rightarrow\dfrac{2^{4-x}}{\left(2^4\right)^5}=\left(2^5\right)^6\)
\(\Rightarrow\dfrac{2^{4-x}}{2^{20}}=2^{30}\)
\(\Rightarrow2^{4-x}=2^{20}\cdot2^{30}\)
\(\Rightarrow2^{4-x}=2^{50}\)
\(\Rightarrow4-x=50\)
\(\Rightarrow x=-46\)
3) \(\dfrac{2^{2x-3}}{4^{10}}=8^3\cdot16^5\)
\(\Rightarrow\dfrac{2^{2x-3}}{\left(2^2\right)^{10}}=\left(2^3\right)^3\cdot\left(2^4\right)^5\)
\(\Rightarrow\dfrac{2^{2x-3}}{2^{20}}=2^{29}\)
\(\Rightarrow2^{2x-3}=2^{49}\)
\(\Rightarrow2x-3=49\)
\(\Rightarrow2x=52\)
\(\Rightarrow x=26\)
DT
1
8 tháng 8 2018
A) \(\left(x-2\right)^2=\dfrac{1}{16}\\ Mà:\left(\dfrac{1}{4}\right)^2=\dfrac{1}{16}hoặc\left(-\dfrac{1}{4}\right)^2=16\\ =>\left(x-2\right)^2=\left(\dfrac{1}{4}\right)^2hoặc\left(x-2\right)^2=\left(-\dfrac{1}{4}\right)^2\\ =>x-2=\dfrac{1}{4}hoặc\left(x-2\right)=-\dfrac{1}{4}\\ =>\left[{}\begin{matrix}x=\dfrac{1}{4}+2\\x=-\dfrac{1}{4}+2\end{matrix}\right.\\ =>\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=\dfrac{7}{4}\end{matrix}\right.\)
23 tháng 8 2019
2) x4 -16 =0 => x4 =16 => x4 = 44 hoặc (-4)4 => x = 4 hoặc -4
VM
14 tháng 11 2019
b) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2=\left(\pm\frac{1}{4}\right)^2\)
\(\Rightarrow x+\frac{1}{2}=\pm\frac{1}{4}.\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}-\frac{1}{2}\\x=\left(-\frac{1}{4}\right)-\frac{1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{-\frac{1}{4};-\frac{3}{4}\right\}.\)
c) \(\left(3x+2\right)^3=-27\)
\(\Rightarrow\left(3x+2\right)^3=\left(-3\right)^3\)
\(\Rightarrow3x+2=-3\)
\(\Rightarrow3x=\left(-3\right)-2\)
\(\Rightarrow3x=-5\)
\(\Rightarrow x=\left(-5\right):3\)
\(\Rightarrow x=-\frac{5}{3}\)
Vậy \(x=-\frac{5}{3}.\)
Chúc bạn học tốt!
\(10.3^x=81\)
\(3^x=80:10\)
\(3^x=8\)
\(\Rightarrow3^x=\varnothing\)
\(20-\left(x-1\right)^3=\frac{1}{16}\)
\(\left(x-1\right)^3=20-\frac{1}{16}\)
\(\left(x-1\right)^3=\frac{320}{16}-\frac{1}{16}\)
\(\left(x-1\right)^3=\frac{319}{16}\)
\(\Rightarrow\left(x-1\right)^3=\varnothing\Leftrightarrow x=\varnothing\)