(4x - 1)^2 = 25.9
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GN
GV Nguyễn Trần Thành Đạt
Giáo viên
16 tháng 10 2023
\(\left(4x-1\right)^2=25.9=225\\ \Leftrightarrow\left(4x-1\right)^2=15^2=\left(-15\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{16}{4}=4\\x=-\dfrac{14}{4}=-\dfrac{7}{2}\end{matrix}\right.\)
H9
HT.Phong (9A5)
CTVHS
16 tháng 10 2023
\(\left(4x-1\right)^2=25\cdot9\)
\(\Rightarrow\left(4x-1\right)^2=5^2\cdot3^2\)
\(\Rightarrow\left(4x-1\right)^2=\left(5\cdot3\right)^2\)
\(\Rightarrow\left(4x-1\right)^2=15^2\)
TH1: \(4x-1=15\)
\(\Rightarrow4x=15+1\)
\(\Rightarrow4x=16\)
\(\Rightarrow x=\dfrac{16}{4}\)
\(\Rightarrow x=4\)
TH2: \(4x-1=-15\)
\(\Rightarrow4x=-15+1\)
\(\Rightarrow4x=-14\)
\(\Rightarrow x=-\dfrac{14}{4}\)
\(\Rightarrow x=-\dfrac{7}{2}\)
N3
2
18 tháng 8 2018
( 5/4x - 2/3 )^4 = 57/16 + 3/2
=> ( 5/4x - 2/3 )^4 = 81/16
=> ( 5/4x - 2/3 )^4 = 3^4/2^4
=> 5/4x - 2/3 = 3/2
=> 5/3x = 13/6
=> x = 13/10
Vậy x = 13/10
TA
18 tháng 8 2018
\(\left(\frac{5}{4}x-\frac{2}{3}\right)^4-\frac{3}{2}=\frac{57}{16}\)
\(\left(\frac{5}{4}x-\frac{2}{3}\right)^4-\frac{3}{2}=\frac{57}{16}+\frac{3}{2}\)
\(\left(\frac{5}{4}x-\frac{2}{3}\right)=\frac{81}{16}\)
Ta xét 2th:
Th1: \(\frac{5}{4}x-\frac{2}{3}=\left(\frac{81}{16}\right)^{\frac{1}{4}}\)
\(\Rightarrow x=\frac{26}{15}\)
Th2: \(\frac{5}{4}x-\frac{2}{3}=-\left(\frac{81}{16}\right)^{\frac{1}{4}}\)
\(\Rightarrow x=-\frac{2}{3}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{26}{15}\\x=-\frac{2}{3}\end{cases}}\)
V
0
NT
0
MH
26 tháng 2 2016
4x2 - 1 = (2x + 1).(3x - 5)
<=> (2x)2 - 12 = (2x + 1).(3x - 5)
<=> (2x - 1).(2x + 1) = (2x + 1).(3x - 5)
<=> (2x - 1).(2x + 1) - (2x + 1).(3x - 5) = 0
<=> (2x + 1).(2x - 1 - 3x + 5) = 0
<=> (2x - 1).(4 - x) = 0
<=> 2x - 1 = 0 hoặc 4 - x = 0
<=> x = 1/2 hoặc x = 4
Vậy S = {1/2; 4}.
HK
1
4 tháng 11 2021
a: \(x\in\varnothing\)
b: \(\Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)
\(\left(4x-1\right)^2=25.9\\ \Leftrightarrow\left(4x-1\right)^2=225\\ \Leftrightarrow\left[{}\begin{matrix}\left(4x-1\right)^2=15^2\\\left(4x-1\right)^2=\left(-15\right)^2\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)
(4x-1)^2=(5/3)^2
Suy ra: 4x-1=5/3
4x=5/3+1
4x=8/3
X=8/3:4
X=....