Tìm n thuộc N biết:
\(\left(7n-11\right)^3=2^5.5^2+200\)
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PK
5
27 tháng 8 2021
(7x−11)3 = 25 . 52 + 200
(7x−11)3 = 32 . 25 + 200
(7x−11)3 = 1000
(7x−11)3 = 103
7x−11 = 10
7x = 10 + 11
7x = 21
x = 21 : 7
x = 3
LA
8
20 tháng 9 2017
a) \(2^x\)\(-\)\(64\)\(=\)\(2^6\)
\(2^x\)\(-\)\(2^6\)\(=\)\(2^6\)
\(2^x\) \(=\)\(2^6\)\(+\)\(2^6\)
\(2^x\) \(=\) \(64\)\(+\)\(64\)
\(2^x\) \(=\) \(128\)
\(\Rightarrow\) \(2^x\) \(=\) \(2^7\)
b) \(\left(7x-11\right)\)\(^3\)\(=\)\(2^5\)\(.\)\(5^2\)\(+\)\(200\)
\(\left(7x-11\right)\)\(^3\)\(=\)\(32\)\(.\)\(25\)\(+\)\(200\)
\(\left(7x-11\right)\)\(^3\)\(=\) \(1000\)
\(\left(7x-11\right)\)\(^3\)\(=\) \(10^3\)
\(\Rightarrow\)\(7x-11\)\(=\)\(10\)
\(7x\) \(=\)\(10+11\)
\(7x\) \(=\) \(21\)
\(x\) \(=\) \(21\)\(:\)\(7\)
\(x\) \(=\) \(3\)
DD
20 tháng 9 2017
\(2^x-64=2^6\)
\(2^x-64=64\)
\(2^x=64+64\)
\(2^x=128\)
\(\)Vì \(128=2^7\) \(\Rightarrow x=7\)
17 tháng 5 2022
\(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=1000\)
\(\Leftrightarrow7x-11=10\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=3\)
17 tháng 5 2022
\(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=800+200\)
\(\Rightarrow\left(7x-11\right)^3=1000=10^3\)
\(\Rightarrow7x-11=10\)
\(\Rightarrow7x=21\)
\(\Rightarrow x=3\)
8 tháng 4 2016
(7x-11)3 = 25.52+ 23.52
(7x-11)3 = 23.52( 22+1)
(7x-11)3 = 23.53=(2.5)3
7x-11=10
x=3
LT
0
DN
4
DH
16 tháng 8 2017
a, \(\left(x-1\right)^3=125\)
\(\Rightarrow x-1=5\Rightarrow x=6\)
b, \(\left(2x+1\right)^3=343\)
\(\Rightarrow2x+1=7\Rightarrow x=3\)
c, \(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=1000\)
\(\Rightarrow7x-11=10\Rightarrow x=3\)
Chúc bạn học tốt!!!
16 tháng 8 2017
a) \(\left(x-1\right)^3=125\Leftrightarrow\left(x-1\right)^3=5^3\Rightarrow x-1=5\)
\(\Leftrightarrow x=6\) vậy \(x=6\)
b) \(\left(2x+1\right)^3=343\Leftrightarrow\left(2x+1\right)^3=7^3\Rightarrow2x+1=7\)
\(\Leftrightarrow2x=6\Leftrightarrow x=\dfrac{6}{2}=3\) vậy \(x=3\)
c) \(\left(7x-11\right)^3=2^5.5^2+200\Leftrightarrow\left(7x-11\right)^3=32.25+200\)
\(\Leftrightarrow\left(7x-11\right)^3=800+200=1000=10^3\Rightarrow7x-11=10\)
\(\Leftrightarrow7x=21\Leftrightarrow x=\dfrac{21}{7}=3\) vậy \(x=3\)
7 tháng 3 2020
Ta có: \(\left(7x-11\right)^3=2^5+5^2+200=1000\)
\(\Rightarrow\left(7x-11\right)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(\Rightarrow7x=21\)
\(\Rightarrow x=3\)
G
7 tháng 3 2020
Trả lời:
\(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=32.25+200\)
\(\Leftrightarrow\left(7x-11\right)^3=800+200\)
\(\Leftrightarrow\left(7x-11\right)^3=1000\)
\(\Leftrightarrow7x-11=10\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=3\)
Vậy\(x=3\)
Hok tốt!
Good girl
LQ
3
8 tháng 10 2021
\(\left(3x-1\right)^3=25\left(3x-1\right)\\ \Leftrightarrow\left(3x-1\right)^2=25\\ \Leftrightarrow\left[{}\begin{matrix}3x-1=5\\3x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\\ \left(3x-14\right)^3=2^5\cdot5^2+200\\ \Leftrightarrow\left(3x-14\right)^3=1000=10^3\\ \Leftrightarrow3x-14=10\Leftrightarrow x=8\)
8 tháng 10 2021
\(\left(3x-1\right)^3=25\left(3x-1\right)\)
\(\Rightarrow\left(3x-1\right)\left(9x^2-6x+1-25\right)=0\)
\(\Rightarrow\left(3x-1\right)\left(9x^2-6x-24\right)=0\)
\(\Rightarrow3\left(3x-1\right)\left(x-2\right)\left(3x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\)
\(\left(3x-14\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(3x-14\right)^3=1000\)
\(\Rightarrow3x-14=10\Rightarrow3x=24\Rightarrow x=8\)
\(\Rightarrow\left(7n-11\right)^3=32\times25+200\)
\(\Rightarrow\left(7n-11\right)^3=1000\)
\(\Rightarrow7n-11=10\)
\(\Rightarrow7n=10+11\)
\(\Rightarrow n=21:7=3\)
\(\left(7n-11\right)^3=2^5.5^2+200\)
\(\left(7n-11\right)^3=32.25+200\)
\(\left(7n-11\right)^3=800+200\)
\(\left(7n-11\right)^3=1000\)
=>TH1:(7n-11)3=103
=>7n-11=10
=>7n=10+11=21
=>n=21:7=3
TH2: (7n-11)3=-103
=>7n-11=-10
=>7n=-10+11
=>7n=1
=>n=1:7=1/7
Mà n thuộc N nên n=3
Kết luận n=3