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1, 4\(^{x+1}\) + 4\(^0\) = 65
\(\Rightarrow\)4\(^{x+1}\) = 65 - 1
\(\Rightarrow\)x + 1 = 64 : 4
\(\Rightarrow\)x + 1 = 16
\(\Rightarrow\)x = 15
2) 10 + 2x = 16\(^{^2}\): 4\(^3\)
\(\Rightarrow\)10 + 2x = 4
\(\Rightarrow\)2x = 4 - 10
\(\Rightarrow\)2x = -6
\(\Rightarrow\)x = -3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,3^n=3^4\)
\(\Rightarrow n=4\)
\(b,2008^n=2008^0\)
\(\Rightarrow n=0\)
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\(\left(4-x:2\right)^3-1=2.\left(2^3-5:2^0\right)+1\)
\(\left(4-x:2\right)^3-1=2\left(8-5:1\right)+1\)
\(\left(4-x:2\right)^3-1=2.3+1\)
\(\left(4-x:2\right)^3-1=7\)
\(\left(4-x:2\right)^3=8\)
\(\left(4-x:2\right)^3=2^3\)
\(4-x:2=2\)
\(x:2=2\)
\(x=4\)
\(\left(4-x\div2\right)^3-1=2.\left(2^3-5\div2^0\right)+1\)
\(\left(4-x\div2\right)^3-1=2.\left(8-5\div1\right)+1\)
\(\left(4-x\div2\right)^3-1=2.\left(8-5\div1\right)+1\)
\(\left(4-x\div2\right)^3-1=2.\left(8-5\right)+1\)
\(\left(4-x\div2\right)^3-1=2.3+1\)
\(\left(4-x\div2\right)^3-1=6+1=7\)
\(\left(4-x\div2\right)^3\approx1,91^3\)
\(4-x\div2\approx1,91\)
\(x\div2=2,09\)
\(\Rightarrow x\approx2,09.2\)
\(\Rightarrow x\approx4,18\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2a/ 2x - 3 = 16 => 2x - 3 = 24 => x - 3 = 4 => x = 7
b/ {x2 - [82 - (52 - 8.3)3 - 7.9]3 - 4.12}3 = 1
=> x2 - [82 - (52 - 8.3)3 - 7.9]3 - 4.12 = 1
=> x2 - [64 - (25 - 8.3)3 - 7.9]3 = 1 + 4.12 = 49
=> x2 - (64 - 13 - 63)3 = 49
=> x2 - 0 = 49
=> x2 = 49
=> x = 7
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bài 2: (x-3).(y+2) = -5
Vì x, y \(\in\)Z => x-3 \(\in\)Ư(-5) = {5;-5;1;-1}
Ta có bảng:
x-3 | 5 | -5 | -1 | 1 |
y+2 | 1 | -1 | -5 | 5 |
x | 8 | -2 | 2 | 4 |
y | -1 | -3 | -7 | 3 |
bài 3: a(a+2)<0
TH1 : \(\orbr{\begin{cases}a< 0\\a+2>0\end{cases}}\)=>\(\orbr{\begin{cases}a< 0\\a>-2\end{cases}}\)=> -2<a<0 ( TM)
TH2: \(\orbr{\begin{cases}a>0\\a+2< 0\end{cases}}\Rightarrow\orbr{\begin{cases}a>0\\a< -2\end{cases}}\Rightarrow loại\)
Vậy -2<a<0
Bài 5: \(\left(x^2-1\right)\left(x^2-4\right)< 0\)
TH 1 : \(\hept{\begin{cases}x^2-1>0\\x^2-4< 0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x^2>1\\x^2< 4\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x>1\\x< 2\end{cases}}\)\(\Rightarrow\)1 < a < 2
TH 2: \(\hept{\begin{cases}x^2-1< 0\\x^2-4>0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x^2< 1\\x^2>4\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x< 1\\x>2\end{cases}}\)\(\Rightarrow\)loại
Vậy 1<a<2
![](https://rs.olm.vn/images/avt/0.png?1311)
1, CÓ( X+1,5)8 VÀ (2,7 -Y)12> HOẶC = 0
MÀ (X+1,5)8 + (2,7-Y)12 =0
SUY RA \(\hept{\begin{cases}X+1,5=0\\2,7-Y=0\end{cases}}\)
SUY RA\(\hept{\begin{cases}X=-1,5\\Y=2,7\end{cases}}\)
(4-x:2)3-1=2.(23-5:20)+1
(4-\(\frac{1}{2}\)x)3-1=2(8-5:1)+1
(4-\(\frac{1}{2}\)x)3-1=2.3+1
(4-\(\frac{1}{2}\)x)3-1=7
(4-\(\frac{1}{2}\)x)3=7+1
(4-\(\frac{1}{2}\)x)3=8
(4-\(\frac{1}{2}\)x)3=23
4-\(\frac{1}{2}\)x=2
8-x=2
-x=4-8
-x=-4
x=4
Vậy x=4
(4 - x : 2)3 - 1 = 2. (23 - 5 : 20) + 1
(4 - x : 2)3 - 1 = 2. (8 - 5 : 1) + 1
(4 - x : 2)3 - 1 = 2. (8 -5) + 1
(4 - x : 2)3 - 1 = 2. 3 + 1
(4 - x : 2)3 - 1 = 6 + 1
(4 - x : 2)3 - 1 = 7
(4 - x : 2)3 = 7 + 1
(4 - x : 2)3 = 8
(4 - x : 2)3 = 23
=> 4 - x : 2 = 2
x : 2 = 4 - 2
x : 2 = 2
x = 2 . 2
x = 4