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1. 3( x - 1 ) - 2 \(\left|x+3\right|\)
= 3x - 3 - 2 ( x + 3 )
= 3x - 3 - 2x - 6
= x - 9
2. \(\left|x-3\right|\) - \(\left|4x-1\right|\)
= x - 3 - ( 4x - 1 )
= x - 3 - 4x + 1 = - 3x - 2
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M = |x - 1| + |1 - 2x|
+ Với \(x\le\frac{1}{2}\) thì |x - 1| = 1 - x; |1 - 2x| = 1 - 2x
Ta có: M = (1 - x) + (1 - 2x)
M = 1 - x + 1 - 2x
M = 2 - 3x
+ Với \(\frac{1}{2}< x< 1\) thì |x - 1| = 1 - x; |1 - 2x| = 2x - 1
Ta có: M = (1 - x) + (2x - 1)
M = 1 - x + 2x - 1
M = x
+ Với \(x\ge1\) thì |x - 1| = x - 1; |1 - 2x| = 2x - 1
Ta có: M = (x - 1) + (2x - 1)
M = x - 1 + 2x - 1
M = 3x - 2
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A = (x - 2)2 + (x + 3)2 - 2.(x + 1)(x - 1)
A = (x - 2)2 + (x + 3)2 - 2.(x2 - 1)
A = x2 - 2.2x + 22 + x2 + 2.3x + 32 - 2x2 + 2
A = 2x + 15
\(A=\left(x-2\right)^2+\left(x+3\right)^2-2\left(x+1\right)\left(x-1\right)\)
\(A=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(A=2x^2+2x+13-2x^2+2\)
\(A=2x+15\)
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(2x - 1)2 + 2(2x - 1)(x + 1) + (x - 1)2 (Dễ dàng nhận thấy đây là HĐT số 1)
= (2x -1 + x - 1)2
= (3x - 2)2
Bài làm
x( 1 - x ) + ( x + 1 )( x - 2 )
= x - x2 + x2 - 2x + x - 2
= ( x + x - 2x ) + ( -x2 + x ) - 2
= -2
Vậy giá trị của đa thức trên là ( -2 )
# Học tốt #