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a) 2x + 1 = 5 - 5x
=> 2x + 5x = 5 - 1
=> 7x = 4
=> x = 4/7
b) 3x - 2 = 2x + 5
=> 3x - 2x = 5 + 2
=> x = 7
c) 7(x - 2) = 5(3x + 1)
=> 7x - 14 = 15x + 5
=> 7x - 15x = 5 + 14
=> - 8x = 19
=> x = - 19/8
d) 2x + 5 = 20 - 3x
=> 2x + 3x = 20 - 5
=> 5x = 15
=> x = 3
e) x - 3 = 18 - 5x
=> x + 5x = 18 + 3
=> 6x = 21
=> x = 21/6 = 7/2
Dạng 1: Rút gọn
Bài 1
a) Rút gọn
P= (\(\dfrac{8}{x^2-16}+\dfrac{1}{x+4}\)):\(\dfrac{1}{x^2-2x-8}\)
= (\(\dfrac{8}{\left(x+4\right)\left(x-4\right)}+\dfrac{x-4}{\left(x+4\right)\left(x-4\right)}\)):\(\dfrac{1}{\left(x-4\right)\left(x+2\right)}\)
= \(\dfrac{x+4}{\left(x+4\right)\left(x-4\right)}:\dfrac{1}{\left(x-4\right)\left(x+2\right)}\)
= \(\dfrac{1}{x-4}.\left(x-4\right)\left(x+2\right)\)
= x+2
Bài 2
a) Rút gọn
D=(\(\dfrac{1}{x-1}-\dfrac{x}{1-x^3}.\dfrac{x^2+x+1}{x+1}\)):\(\dfrac{2x+1}{x^2+x+1}\)
= (\(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\)):\(\dfrac{2x+1}{x^2+x+1}\)
= \(\dfrac{2x+1}{\left(x+1\right)\left(x-1\right)}\).\(\dfrac{x^2+x+1}{2x+1}\)
= \(\dfrac{x^2+x+1}{\left(x+1\right)\left(x-1\right)}\)
b) Tìm x∈Z để D∈Z
D=\(\dfrac{x^2+x+1}{\left(x+1\right)\left(x-1\right)}=\dfrac{x^2+x+1}{x^2-1}=\dfrac{x^2-1}{x^2-1}+\dfrac{x+2}{x^2-1}=1+\dfrac{x+2}{x^2-1}\)Để D nguyên thì x+2=0⇔x=-2(t/m)
Vậy ...........................
Dạng 2: Phương trình
Bài 1. Giải phương trình
a) 2x+1=5-5x
⇔ 2x+5x=5-1
⇔ 7x=4
⇔ x=\(\dfrac{4}{7}\)
Vậy S=\(\left\{\dfrac{4}{7}\right\}\) là tập nghiệm của hương trình
b) 3x-2=2x+5
⇔ 3x-2x=5+2
⇔ x=7
Vậy......................
c) 7(x-2)=5(3x+1)
⇔ 7x-14=15x+5
⇔ 7x-15x=5+14
⇔ -8x=19
⇔ x=-\(\dfrac{19}{8}\)
Vậy..........................
d) 2x+5=20-3x
⇔ 2x+3x=20-5
⇔ 5x=15
⇔ x=3
Vậy...................
e) x-3=18-5x
⇔ x+5x=18+3
⇔ 6x=21
⇔ x=\(\dfrac{7}{2}\)
Vậy..............................
dài lắm nên mình làm tắt
1) (x - 5)^2 + (x + 3)^2 = 2(x - 4)(x + 4) - 5x + 7
<=> x^2 - 10x + 25 + x^2 + 6x + 9 = 2x^2 + 8x - 8x - 32 - 5x + 7
<=> 2x^2 - 4x + 34 = 2x^2 - 5x - 25
<=> -4x + 34 = -5x - 25
<=> x + 34 = -25
<=> x = -25 - 34
<=> x = - 59
2) (x + 3)(x - 2) - 2(x + 1)^2 = (x - 3)^2 - 2x^2 + 4x
<=> x^2 - 2x + 3x - 6 - 2x^2 - 4x - 2 = x^2 - 6x + 9 - 2x^2 + 4x
<=> -x^2 - 3x - 8 = -x^2 - 2x + 9
<=> -3x - 8 = -2x + 9
<=> -x - 8 = 9
<=> -x = 9 + 8
<=> x = -17
3) (x + 1)^3 - (x + 2)(x - 4) = (x - 2)(x^2 + 2x + 4) + 2x^2
<=> x^3 + 2x^3 + x + x^2 + 2x + 1 - x^2 + 4x - 2x + 8 = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 + 2x^2
<=> 2x^2 + 5x + 9 = 2x^2 - 8
<=> 5x + 9 = -8
<=> 5x = -8 - 9
<=> 5x = -17
<=> x = -17/5
4) (x - 2)^3 + (x - 5)(x + 5) = x(x^2 - 5x) - 7x + 3
<=> x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 + x^2 - 5^2 = x^3 - 5x^2 - 7x + 3
<=> 12x - 33 = -7x + 3
<=> 19x - 33 = 3
<=> 19x = 3 + 33
<=> 19x = 36
<=> x = 36/19
5) (x + 4)(x^2 - 4x + 16) - x(x - 4)^2 = 8(x - 3)(x + 3)
<=> x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 - x^3 + 8x^2 - 16x = 8x^2 - 72
<=> -16x + 64 = -72
<=> -16x = -72 - 64
<=> -16x = -136
<=> x = 136/16 = 17/2
6) 4(x - 1)(x + 2) - 5(x + 7) = (2x + 3)^2 - 5x + 3
<=> 4x^2 + 8x - 4x - 8 - 5x - 35 = 4x^2 + 12x + 9 - 5x + 3
<=> -x - 43 = 7x + 12
<=> -8x - 43 = 12
<=> -8x = 12 + 43
<=> -8x = 55
<=> x = -55/8
7) (x - 1)(x^2 + x + 1) + 3(x - 2)^2 = x(x^2 + 3x - 1)
<=> x^3 + x^2 + x - x^2 - x - 1 + 3x^2 - 12x + 12 = x^3 + 3x^2 - x
<=> 3x^2 - 12x + 11 = 3x^2 - x
<=> -12x + 11 = -x
<=> 11 = -x + 12x
<=> 11 = 11x
<=> x = 1
8) (x + 5)(x - 5) - (x + 3)(x^2 - 3x + 9) = 5 - x(x^2 - x - 2)
<=> x^2 - 25 - x^3 + 3x^2 - 9 - 3x^2 + 9x - 27 = 5 - x^3 + x^2 + 2x
<=> -52 - x^3 = 5 - x^3 + 2x
<=> -52 = 5x + 2x
<=> -5x - 2x = 52
<=> -7x = 52
<=> x = -52/7
9) (x + 2)^2 - 2(x + 3)(x - 4) = 5 - x(x - 3)
<=> x^2 + 4x + 4 - 2x^2 + 8x - 6x + 24 = 5 - x^3 + 3x
<=> 6x + 28 = 5 + 3x
<=> 6x + 28 - 3x = 5
<=> 3x + 28 = 5
<=> 3x = 5 - 28
<=> 3x = -23
<=> x = -23/3
10) (x + 7)(x - 7) - (x + 2)^2 = 5(x - 2) + (x - 7)
<=> x^2 - 49 - x^2 - 4x - 4 = 5x - 10 + x - 7
<=> -53 - 4x = 6x - 17
<=> -4x = 6x + 36
<=> -4x - 6x = 36
<=> -10x = 36
<=> x = -36/10 = -18/5
a) x2 - 5x - y2 -5y
= ( x2 - y2 ) + ( -5x - 5y)
= ( x - y ) ( x + y) - 5( x + y )
= ( x + y ) ( x - y -5)
b) x3 + 2x2 - 4x - 8
= x2 ( x + 2 ) - 4 ( x + 2 )
= ( x +2 ) ( x2 -4 )
= ( x+2)2 ( x-2)
Bai 2 :
a, \(A=\left(x+3\right)^2+\left(x-2\right)^2-2\left(x+3\right)\left(x-2\right)\)
\(=x^2+6x+9+x^2-4x+4-2\left(x^2-2x+3x-6\right)\)
\(=2x^2+2x+13-2x^2-2x+12=25\)
b, \(B=\left(x-2\right)^2-x\left(x-1\right)\left(x-3\right)+3x^2-9x+8\)
\(=x^2-4x+4-x\left(x^2-3x-x+3\right)+3x^2-9x+8\)
\(=4x^2-13x+12-x^3+4x^2-3x=-16x+12-x^3\)
a) \(A=\left(3x+2\right)^2-9x\left(x+1\right)\)
\(A=9x^2+12x+4-9x^2-9x\)
\(A=3x+4\)
\(B=\left(2x-1\right)^2-2\left(2x-1\right)\left(5x-1\right)+\left(5x-1\right)^2\)
\(B=\left[2x-1-\left(5x-1\right)\right]^2\)
\(B=\left(2x-1-5x+1\right)^2\)
\(B=\left(-3x\right)^2\)
\(B=9x^2\)
bài 1.
a.\(A=x^2-2xy+y^2+x^2+2xy+y^2=2\left(x^2+y^2\right)\)
b.\(B=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)=4xy\)
c.\(C=4a^2+4ab+b^2-\left(4a^2-4ab+b^2\right)=8ab\)
d.\(D=4x^2-4x+1-2\left(4x^2-12x+9\right)+4=-4x^2+20x-13\)
.bài 2
a.\(A=x^2+6x+9+x^2-9-2\left(x^2-2x-8\right)=10x+16;x=-\frac{1}{2}\Rightarrow A=9\)
b.\(B=9x^2+24x+16-x^2+16-10x=8x^2+14x+32\Rightarrow x=-\frac{1}{10}\Rightarrow B=\frac{767}{25}\)
c.\(C=x^2+2x+1-\left(4x^2-4x+1\right)+3\left(x^2-4\right)=6x-12\Rightarrow x=1\Rightarrow C=-6\)
d.\(D=x^2-9+x^2-4x+4-2x^2+8x=4x-5\Rightarrow x=-1\Rightarrow A=-9\)
Trả lời:
Bài 1: Rút gọn biểu thức:
a) A = ( x - y )2 + ( x + y )2
= x2 - 2xy + y2 + x2 + 2xy + y2
= 2x2 + 2y2
b) B = ( x + y )2 - ( x - y )2
= x2 + 2xy + y2 - ( x2 - 2xy + y2 )
= x2 + 2xy + y2 - x2 + 2xy - y2
= 4xy
c) C = ( 2a + b )2 - ( 2a - b )2
= 4a2 + 4ab + b2 - ( 4a2 - 4ab + b2 )
= 4a2 + 4ab + b2 - 4a2 + 4ab - b2
= 8ab
d) D = ( 2x - 1 )2 - 2 ( 2x - 3 )2 + 4
= 4x2 - 4x + 1 - 2 ( 4x2 - 12x + 9 ) + 4
= 4x2 - 4x + 1 - 8x2 + 24x - 18 + 4
= - 4x2 + 20x - 13
Bài 2: Rút gọn rồi tính giá trị biểu thức:
a) A = ( x + 3 )2 + ( x - 3 )( x + 3 ) - 2 ( x + 2 )( x - 4 )
= x2 + 6x + 9 + x2 - 9 - 2 ( x2 - 2x - 8 )
= 2x2 + 6x - 2x2 + 4x + 16
= 10x + 16
Thay x = 1/2 vào A, ta có:
\(A=10.\left(-\frac{1}{2}\right)+16=-5+16=11\)
b) B = ( 3x + 4 )2 - ( x - 4 )( x + 4 ) - 10x
= 9x2 + 24x + 16 - x2 + 16 - 10x
= 8x2 + 14x + 32
Thay x = - 1/10 vào B, ta có:
\(B=8.\left(-\frac{1}{10}\right)^2+14.\left(-\frac{1}{10}\right)+32=\frac{767}{25}\)
c) C = ( x + 1 )2 - ( 2x - 1 )2 + 3 ( x - 2 )( x + 2 )
= x2 + 2x + 1 - 4x2 + 4x - 1 + 3 ( x2 - 4 )
= - 3x2 + 6x + 3x2 - 12
= 6x - 12
Thay x = 1 vào C, ta có:
\(C=6.1-12=-6\)
d) D = ( x - 3 )( x + 3 ) + ( x - 2 )2 - 2x ( x - 4 )
= x2 - 9 + x2 - 4x + 4 - 2x2 + 8x
= 4x - 5
Thay x = - 1 vào D, ta có:
\(D=4.\left(-1\right)-5=-9\)
a, ĐKXĐ : x khác -4;4;-2
P =[ 8+x-4/(x-4).(x+4) ] : 1/(x+2).(x-4)
= x+4/(x+4).(x-4) . (x+2).(x-4)
= x+2
b, x^2-9x+20 = 0
<=> (x^2-4x)-(5x-20)=0
<=> (x-4).(x-5)=0
<=> x-4=0 hoặc x-5=0
<=> x=4 hoặc x=5
+, Với x=4 thì P = 4+2 = 6
+, Với x=5 thì P = 5+2 = 7
k mk nha
`Answer:`
`a)`
`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`
`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`
`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`
`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`
`=>A=-2x^2+28x-6`
`b)`
`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`
`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`
`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`
`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`
Thay `x=-7` vào ta được:
`B=10(-7)^2-2(-7)^3-7(-7)-6`
`=>B=10.49-2(-343)+49-6`
`=>B=490+686+49-6`
`=>B=1219`