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b,(723+277).2001-(456+544).1010-389-611
=1000.2001-1000.1010-(389+611)
=1000.2001-1000.1010-1000
=1000.(2001-1010-1)
=1000.990
=990000
a, 92.53+12.92-81+36.92
=92.(53+12+36)-81
=81.101-81
=8181-81
=8100
(2774+1026):38 + (25.4).7.5
= 3800 : 38 + 100.35
= 100 + 3500
= 3600
a,2774:38+1026:38+25.7.4.5
=(2774+1026):38+3500
=3800:38+3500
=100+3500
=3600
2774:38+1026:38+25.7.4.5
= (2774+1026):38+25.7.4.5
=3800:38+25.7.4.5
=100+25.7.4.5
=100+(25.4).(7.5)
=100+100.35
=100+3500
= 3600
a) 20-( x - 5 ) x2 = 2
( x - 5 ) x2 = 20-2=18
x - 5 = 18 : 2
x - 5 = 9
x = 9+5
x = 14.
b) 150 : ( 38 - 2x ) = 5
38 - 2x = 150 : 5 = 30
2x = 38 - 30 = 8
x = 8 : 2
x = 4.
a) (x2 - 7).(x2 - 38) < 0
\(\Leftrightarrow\hept{\begin{cases}x^2-7>0\\x^2-38< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x^2>7\\x^2< 38\end{cases}}\Leftrightarrow7< x^2< 38\Leftrightarrow3\le x\le6\)
Hoặc \(\hept{\begin{cases}x^2-7>0\\x^2-38< 0\end{cases}}\)(Vô lý)
=> \(3\le x\le6\)
b) \(\left|x-3\right|+\left|x^2-9\right|=0\)
\(\Leftrightarrow\hept{\begin{cases}\left|x-3\right|=0\\\left|x^2-9\right|=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x^2=9\end{cases}}\)
Ở trường hợp x2 = 9
=> \(x=\orbr{\begin{cases}3\\-3\end{cases}}\)
Vậy \(x=\orbr{\begin{cases}3\\-3\end{cases}}\)
Lời giải:
a. $(3x+9)^{40}=49(3x+9)^{38}$
$(3x+9)^{40}-49(3x+9)^{38}$
$(3x+9)^{38}[(3x+9)^2-49]=0$
$\Rightarrow (3x+9)^{38}=0$ hoặc $(3x+9)^2-49=0$
Nếu $(3x+9)^{38}=0$
$\Rightarrow 3x+9=0$
$\Rightarrow x=-3$
Nếu $(3x+9)^2-49=0$
$\Rightarrow (3x+9)^2=49=7^2=(-7)^2$
$\Rightarrow 3x+9=7$ hoặc $3x+9=-7$
$\Rightarrow x=\frac{-2}{3}$ hoặc $x=\frac{-16}{3}$
b/
Xét $A=2^x+2^{x+1}+2^{x+2}+....+2^{x+2015}$
$2A=2^{x+1}+2^{x+2}+2^{x+3}+....+2^{x+2016}$
$\Rightarrow 2A-A=(2^{x+1}+2^{x+2}+2^{x+3}+....+2^{x+2016})-(2^x+2^{x+1}+2^{x+2}+....+2^{x+2015})$
$\Rightarrow A=2^{x+2016}-2^x$
Vậy $2^{x+2016}-2^x=2^{2019}-8$
$\Rightarrow 2^x(2^{2016}-1)=2^3(2^{2016}-1)$
$\Rightarrow 2^x=2^3$
$\Rightarrow x=3$
Bài 1:
a) (2^9 . 3 + 2^9 . 5) : 2^12
= [2^9 . (3 + 5)] : 2^12
= [2^9 . 8] : 2^12
= [2^9 . 2^3] : 2^12
= 2^12 : 2^12
= 1
b) 13^2 - (5^2 . 4 + 2^2 . 15)
= 13^2 - (5^2 . 4 + 4 . 15)
= 13^2 - [4 . (5^2 + 15)]
= 13^2 - [4 . (25 + 15)]
= 13^2 - [4 . 40]
= 13^2 - 160
= 13^2 - 40^2
= -27^2
= 729
Bài 2:
a) 30 . (2^2 . 15 - x) = 30
2^2 . 15 - x = 30 : 30
2^2 . 15 - x = 1
4 . 15 = 1 + x
60 = 1 + x
=> x = 60 - 1
x = 59
Bài 2:
b) 2^4 . 38 - 2^4 . x = 16
16 . (38 - x) = 16
38 - x = 16 : 16
38 - x = 1
x = 38 - 1
x = 37
c) (7 . x - 11^3) = 2^5 . 5^2 + 200
(7 . x - 11^3) = 2^5 . 5^2 + 5^2 . 2^3
(7 . x - 11^3) = 5^2 . (2^5 + 2^3)
(7 . x - 11^3) = 25 . 40
(7 . x - 1331) = 1000
7 . x = 1000 + 1331
7 . x = 2331
x = 2331 : 7
x = 333.
A = ( 6888 : 56 - 112 ) . 152 _ 13 . 72 + 13 . 28
A = ( 123 - 121 ) . 152 - 13 . ( 72 + 28 )
A = 2 . 152 - 13 . 100
A = 13.100 - 304
A = 1300 - 304
A = 996
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