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\(\left(2x-1\right)^{x-4}=\left(x+2\right)^{x-4}=>2x-1=x+2=>\left(2x-x\right)=1+2=>x=3\)
\(=>2\cdot4^x+64\cdot4^x=1056\)
\(=>4^x\cdot\left(2+64\right)=1056\)
\(=>4^x=1056:66=16\)
\(=>4^x=4^2\)
\(=>x=2\)
ti ck nha
2.22x + 43.4x = 1056
=> 2.4x + 43.4x = 1056
=> (2 + 64).4x = 1056
=> 66.4x = 1056
=> 4x = 1056 : 66
=> 4x = 16
=> 4x = 42
=> x = 2
7.4x - 1 + 4x + 1 = 23
=> 7.4x.1/4 + 4x.4 = 23
=> (7/4 + 4).4x = 23
=> 23/4.4x = 23
=> 4x = 23 : 23/4
=> 4x = 4
=> x = 1
3x + 2 - 5.3x = 36
=> 3x.9 - 5.3x = 36
=> 3x.(9 - 5) = 36
=> 3x.4 = 36
=> 3x = 36 : 4
=> 3x = 9 = 32
=> 3x = 2
1) 2x+1+2x=2x(2+1)=24
=>2x=8 =>x=3
2) 4x+1-3.4x=4x(4-3)=>4x=16=>x=2
3) x2-x=x(x-1)=0
=>\(\orbr{\begin{cases}x=0\\x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
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
1, xy-2x+3y=9
<=> xy-2x+3y-9=0
<=> x(y-2) + 3(y-2)=0
<=>(y-2)(x+3)=0
<=>+) y-2=0 <=> y=2
+)x+3=0<=>x=-3
a, 2x . 4 = 128
2x = 128 : 4
2x = 32
2x = 25
=> x = 5
b, x15 = x1
=> x15 - x = 0
x . ( x14 - 1 ) = 0
=> x = 0 hoặc x14 - 1 = 0
=> x = 0 hoặc x = 1
c, (2x + 1)3 = 125
( 2x + 1 )3 = 53
=> 2x + 1 = 5
=> 2x = 5 - 1
=> 2x = 4
=> x = 4 : 2
=> x = 2
d, (x – 5)4 = (x - 5)6
=> ( x - 5 )6 - ( x - 5 )4 = 0
=> ( x - 5 )4 . [ ( x - 5 )2 - 1 ] = 0
=> \(\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}}\)
e, x10 = x
x10 - x = 0
x . ( x9 - 1 ) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\x^9-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
f, (2x -15)5 = (2x -15)3
( 2x - 15 )5 - ( 2x - 15 )3 = 0
( 2x - 15 )3 . [ ( 2x - 15 )2 - 1 ] = 0
\(\Rightarrow\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}\Rightarrow\orbr{\begin{cases}2x-15=0\\2x-15=1\end{cases}\Rightarrow}\orbr{\begin{cases}x\text{ không tồn tại}\\x=8\end{cases}}}\)
Ta có: \(x^2+2x+6\)
\(=x.\left(x+4\right)-2x+6\)
\(=x.\left(x+4\right)-2.\left(x+4\right)+14\)
mà \(x.\left(x+4\right)-2.\left(x+4\right):\left(x+4\right)\)
Để \(x^2+2x+6:\left(x+4\right)\) thì \(14:\left(x+4\right)\) \(\implies\)\(\left(x+4\right)\)\(\in\)Ư(14)=\(\{\)\(1;-1;2;-2;7;-7;14;-14\)\(\}\)
\(\implies\) x\(\in\) \(\{\) \(-3;-5;-2;-6;3;-11;10;-18\) \(\}\)
Vậy với các số nguyên x \(\in\) \(\{\) \(-3;-5;-2;-6;3;-11;10;-18\) \(\}\) thì \(x^2+2x+6\) là bội của \(\left(x+4\right)\)