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a.|x-1|=5
=> hai TH
x-1=5 =>x=5+1=6
x-1=-5 => x= -5+1=-4
b. x2 = 52
=> x=5
a ) | x - 1 | = 5
+ x - 1 = 5 hoặc x -1 = -5 + x - 1 = 5 x = 5 + 1 x = 6 + x - 1 = -5 x = -5 + 1 x = -4 Vậy x = 6 hoặc x = -4 b, \(x^2=25\) \(x^2=5^2\) => x = 5 c) 3 . ( x - 2 ) = 5 . ( x + 1 ) 3x - 6 = 5x + 5 -5 - 6 = 5x - 3x -11 = 2x x = -11 : 2 x = \(\dfrac{-11}{2}\)d) 3. x + 5\(^{94}\) : 5\(^{92}\) = 3\(^2\) + 8
3x + \(5^2\) = 9 + 8
3x + 25 = 17
3x = 17 - 25
3x = -8
x = -8 : 3
x = \(\dfrac{-8}{3}\)
Bài 1 :
( 2X - 1 )3 = 27
( 2X - 1 )3 = 33
<=> 2X - 1 = 3
<=> 2X = 4
<=> X = 2
Bài 2 ;
Dãy số 2 ; 4 ; 6 ; ........ ; 98 ; 100 có số các số hạng là :
( 100 - 2 ) : 2 + 1 = 50 ( số hạng )
Trung bình cộng của dãy số 2 ; 4 ; 6 ; ......; 98 ; 100 là :
\(\frac{\left(100+2\right).50}{2}:50=51\)
Bài 3
a) \(2^x.4=64\Leftrightarrow2^x=64:4\Leftrightarrow2^x=16\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)
Các phần còn lại bạn làm tương tự như phần a
Bài 1:
\(\left(2x-1\right)^3=27\)=> \(2x-1=3\)=> 2x = 3+1 = 4 => x = 2
Bài 2: Trung bình cộng của dãy số đó là: \(\frac{\left(2+100\right).50:2}{50}=102:2=51\)
Bài 3: a) \(2^x.4=64\)=> \(2^x=64:4=16=2^4\)=> x = 4
b) \(5^{x+1}-5^x=100\)=> \(5^x.\left(5-1\right)=100\)=> \(5^x.4=100\)
=> \(5^x=\frac{100}{4}=25=5^2\)=> x = 2
c) \(5^{2x+2}-19.5^2=6.5^2\)=> \(5^{2x+2}=6.5^2+19.5^2=625=5^4\)=> 2x + 2 = 4 => x = 1
d) \(\left(x-1\right)^2=9\)=> x - 1 = 3 hoặc x - 1 = -3 => x = 4 hoặc x = -2
e) \(\left(x-2\right)^3=8\)=> x - 2 = 2 => x = 4
a) Ta có: \(\frac{9}{25}=\left(\frac{3}{5}\right)^2=\left(\frac{-3}{5}\right)^2\)
TH1: \(\Rightarrow\left(2x+\frac{3}{5}\right)^2=\left(\frac{3}{5}\right)^2\)
\(\Rightarrow2x+\frac{3}{5}=\frac{3}{5}\)
\(\Rightarrow2x=0\)
\(\Rightarrow x=0\)
TH2: \(2x+\frac{3}{5}=\frac{-3}{5}\Rightarrow2x=\frac{-6}{5}\Rightarrow x=\frac{-3}{5}\)
b) \(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)
\(\Rightarrow3\left(3x-\frac{1}{2}\right)^3=\frac{-1}{9}\)
\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\frac{-1}{27}\)
Mà \(\frac{-1}{27}=\left(-\frac{1}{3}\right)^3\)
\(\Rightarrow3x-\frac{1}{2}=\frac{-1}{3}\Leftrightarrow3x=\frac{1}{6}\Rightarrow x=\frac{1}{18}\)
c) \(-5\left(x+\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{2}{3}x-\frac{5}{6}\)
\(\Rightarrow-5x-1-\frac{1}{2}x+\frac{1}{3}-\frac{2}{3}x+\frac{5}{6}=0\)
\(\Rightarrow-\frac{37}{6}x=\frac{-1}{6}\Rightarrow x=\frac{1}{37}\)
d) \(3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=x+\frac{1}{5}\)
\(\Rightarrow3x-\frac{3}{2}-5x-3-x-\frac{1}{5}=0\)
\(\Rightarrow-3x=\frac{47}{10}\Rightarrow x=\frac{-47}{30}\)
a) 2(x-1)^2=800 5^x+1.5^5=5^9
(x-1)^2=800:2 5^x.5.5^5=5^9
(x-1)^2=400 5^x.5^6=5^9
(x-1)^2=20^2 5^x=5^9:5^6
(x-1)=20 5^x=5^3
x=20+1 => x=3
x=21
c) 25^2 : 5(x-1)=25 d)4^x . 7 +8^2=176
625:5(x-1)=25 4^x . 7+64=176
5(x-1)=625:25 4^x . 7=176:64
5(x-1)=25 4^x . 7=112
x-1=25:5 4^x =112:7
x-1=5 4^x=16
x=5+1 mà 16=4^2
x=6 =>4^x=4^2
=>x=2
bài e) mình ko biết !! ^.^
\(a.2^x=32\Leftrightarrow2^x=2^5\Leftrightarrow x=5\)
\(b.\left(x-5\right)^3=8\Leftrightarrow\left(x-5\right)^3=2^3\Leftrightarrow x-5=2\Leftrightarrow x=7\)
\(c.5^{x+1}=25\Leftrightarrow5^{x+1}=5^2\Leftrightarrow x+1=2\Leftrightarrow x=1\)
\(d.3\cdot\left(6x+3\right)=3^5\)
\(\Leftrightarrow6x+3=3^4\)
\(\Leftrightarrow6x=3^4-3=81-3=78\)
\(\Leftrightarrow x=78:613\)
Bài 1 câu a:
1/-8 + -5/8
= -1/8 - 5/8
= -6/8
= -3/4
Câu b:
-1/21 + -1/28
= -4/84 - 3/84
= - 7/854
Câu c:
-5/9 + 8/15 + -2/11 + 4/-9 + 7/15
= (8/15+ 7/15) - (5/9 + 4/9) - 2/11
= 1 - 1 - 2/11
= 0 - 2/11
= - 2/11
Câu d:
-25/-75 + 17/34 + 121/- 132
= 1/3 + 1/2 - 11/12
= 4/12 + 6/12 - 11/12
= 10/12 - 11/12
= - 1/12
Bài 2a:
51/23 = 5151/2323 = 515151/232323
\(\frac{5151}{2323}\) = \(\frac{5151:101}{2323:101}\) = \(\frac{51}{23}\) (1)
\(\frac{515151}{232323}\) = \(\frac{515151:10101}{232323:10101}\) = \(\frac{51}{23}\) (2)
Từ (1) và (2) ta có:
\(\frac{51}{23}=\frac{5151}{2323}=\frac{515151}{232323}\) (đpcm)
\(\left|x-1\right|=5\)
<=> \(\hept{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)
<=> \(\hept{\begin{cases}x=6\\x=-4\end{cases}}\)
\(x^2=25\)
<=> \(\hept{\begin{cases}x=5\\x=-5\end{cases}}\)
\(3\left(x-2\right)=5\left(x+1\right)\)
<=> \(3x-6=5x+5\)
<=> \(-2x=11\)
<=> \(x=\frac{-11}{2}\)
\(3x+5^{94}:5^{92}=3^2+8\)
<=> \(3x+25=9+8\)
<=> \(3x=-8\)
<=> \(x=\frac{-8}{3}\)
\(a)|x-1|=5\)
\(\Leftrightarrow\hept{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=6\\x=-4\end{cases}}\)
\(b)x^2=25\)
\(\Leftrightarrow\hept{\begin{cases}x=5\\x=-5\end{cases}}\)
\(c)3\times\left(x-2\right)=5\times\left(x+1\right)\)
\(\Leftrightarrow3x-6=5x+5\)
\(\Leftrightarrow-2x=11\)
\(\Leftrightarrow x=\frac{-11}{2}\)
\(d)3\times x+5^{94}\div5^{92}=3^2+8\)
\(\Leftrightarrow3x+25=9+8\)
\(\Leftrightarrow3x=-8\)
\(\Leftrightarrow x=\frac{-8}{3}\)
a) \(\left|x-1\right|=5\)
\(\Rightarrow\hept{\begin{cases}x-1=5\\x-1=-5\end{cases}}\Rightarrow\hept{\begin{cases}x=6\\x=-4\end{cases}}\)
Vậy ....
b) \(x^2=25\)
\(\Rightarrow x=\pm5\)
c) \(3\left(x-2\right)=5\left(x+1\right)\)
\(\Rightarrow3x-6=5x+5\)
\(\Rightarrow3x-5x=6+5\)
\(\Rightarrow-2x=11\)
\(\Rightarrow x=\frac{-11}{2}\)
d, \(3x+5^{94}:5^{92}=3^2+8\)
\(\Rightarrow3x+5^2=9+8\)
\(\Rightarrow3x+25=17\)
\(\Rightarrow3x=-8\)
\(\Rightarrow x=\frac{-8}{3}\)
a) \(|x-1|=5\)
\(\Rightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)
Vậy x = 6 hoặc x = -4
b) \(x^2=25\)
\(\Rightarrow x^2=5^2\)
\(\Rightarrow x=5\)
Vậy x = 5
c) \(3\left(x-2\right)=5\left(x+1\right)\)
\(\Rightarrow3x-6=5x+5\)
\(\Rightarrow3x-5x=6+5\)
\(\Rightarrow-2x=11\)
\(\Rightarrow x=11:-2\)
\(\Rightarrow x=\frac{-11}{2}\)
Vậy \(x=\frac{-11}{2}\)
d) \(3x+5^{94}:5^{92}=3^2+8\)
\(\Rightarrow3x+5^2=9+8\)
\(\Rightarrow3x+25=17\)
\(\Rightarrow3x=17-25\)
\(\Rightarrow3x=-8\)
\(\Rightarrow x=-8:3\)
\(\Rightarrow x=\frac{-8}{3}\)
Vậy \(x=\frac{-8}{3}\)
_Chúc bạn học tốt_
\(a.\left|x-1\right|=5\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)
Vậy \(x\in\left\{6;\left(-4\right)\right\}\)
\(b.x^2=25\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\x=-5\end{cases}}\)
Vậy \(x\in\left\{5;\left(-5\right)\right\}\)
\(c.3.\left(x-2\right)=5.\left(x+1\right)\)
\(3.x-6=5.x+5\)
\(3.x-5.x=6+5\)
\(-2x=11\)
\(x=\frac{-11}{2}\)
Vậy \(x=\frac{-11}{2}\)
\(d.3.x+5^{94}:5^{92}=3^2+8\)
\(3x+5^2=9+8\)
\(3x+25=17\)
\(3x=-8\)
\(x=\frac{-8}{3}\)
Vậy \(x=\frac{-8}{3}\)