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Bài 1: a) (2x+1)2 = 25
(2x+1)2 = 52
=> 2x + 1 = 5 hoặc 2x+1 = -5
=> x=2 hoặc x=-3
b) 2x+2 - 2x = 96
<=> 2x . 22 - 2x = 96
<=> 2x(4-1) =96
<=>2x = 96 :3 = 32 = 25
<=> x = 5
c) (x-1)3 = 125
<=> (x-1)3 = 53
<=> x-1=5
<=>x= 5 +1 = 6
A = \(4\left(x-5\right)-x^2\left(x+1\right)-x^3\left(x-3\right)-\left(x-4+x^2\right)\)
A = \(4x-20-x^3-x^2-x^4+3x^3-x+4-x^2\)
A = \(-x^3-3x^3-x^2+x^2-x^4+4x-x-20+4\)
A = \(-4x^3-x^4+4x-16\)
B = \(-3\left(x^2-x+1\right)-2\left(4-x^2\right)-6\left(x+1\right)-x^4-x^3\)
B = \(-3x^2+3x-3-8+2x^2-6x-6-x^4-x^3\)
B = \(-x^4-x^3-3x^2-2x^2+3x-6x-3-8-6\)
B = \(-x^4-x^3-5x^2-3x-17\)
C = \(-\left(x^4+3x^2-2\right)-x^2\left(5-x\right)+3\left(x-1\right)\)
C = \(-x^4-3x^2+2-5x^2+x^3+3x-3\)
C = \(-x^4+x^3-3x^2+5x^2+3x+2-3\)
C = \(-x^4+x^3-2x^2+3x-1\)
#Yiin
\(A=4x-20-x^3-x-x^4+3x^3-x+4-x^2\)
\(=-x^4+2x^3-x^2+2x-16\)
\(B=-3x^2+3x-3-8+2x^2-6x-6-x^4-x^3\)
\(=-x^4-x^3-x^2-3x-17\)
\(C=-x^4-3x^2+2-5x^2+x^3+3x-3\)
\(=-x^4+x^3-8x^2+3x-1\)
Từ đó có:
\(A-B=-x^4+2x^3-x^2+2x-16-\left(-x^4-x^3-x^2-3x-17\right)\)
\(=-x^4+2x^3-x^2+2x-16+x^4+x^3+x^2+3x+17\)\(=3x^3+5x+1\)
\(B-C=-x^4-x^3-x^2-3x-17-\left(-x^4+x^3-8x^2+3x-1\right)\)
\(=-x^4-x^3-x^2-3x-17+x^4-x^3+8x^2-3x+1\)
\(=-2x^3+7x^2-6x-16\)
\(C-A=-x^4+x^3-8x^2+3x-1-\left(-x^4+2x^3-x^2-2x-16\right)\)
\(=-x^4+x^3-8x^2+3x-1+x^4-2x^3+x^2+2x+16\)
\(=-x^3-7x^2+5x+15\)
Bài 1:
a) 2|x-1| = 24.64
=> 2|x-1|= 210
=> |x-1|=10
=> \(\left[{}\begin{matrix}x-1=10\\x-1=-10\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=11\\x=-9\end{matrix}\right.\)
Vậy...
b)(3x-1)4=16
=> (3x-1)4=24
=> 3x - 1=2
=> 3x = 3
=> x=1
Vậy...
c) (2x+1)4=(2x+1)6
=> (2x+1)4 - (2x+1)6=0
=> (2x+1)4.[1 - (2x+1)2 ] = 0
=> \(\left[{}\begin{matrix}\left(2x+1\right)^4=0\\1-\left(2x+1\right)^2=0\end{matrix}\right.\)
+) (2x+1)4=04
=> 2x+1=0
=> 2x = -1
=> x= \(\frac{-1}{2}\)
+) 1 - (2x+1)2=0
=> (2x+1)2 = 1
=> \(\left[{}\begin{matrix}2x+1=1\\2x+1=-1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
Vậy...
d) x13=27.x10
=> x3=33
=> x=3
e)2x+2x+3=144
=> 2x(1+8)=144
=> 2x= 16 = 24
=> x=4
Bài 2:
a) Hình như đề bài là thế này:
CMR: 55-54+53 chia hết cho 7
Xét 55-54+53
=53(52-5+1)
=53. 21
Mà 21\(⋮\)7 => 53.21 chia hết cho 7 hay 55-54+53
Vậy...
b) Xét 76+75-74
= 74(72+7-1)
=74.55
Mà 55 \(⋮\)11 => 74.55 chia hết cho 11 hay 76+75-74 chia hết cho 7
Vậy...