5.x-(23+22)=4
1) (x+5)2
2) (2x-5y)2
3) (x+8) (x-8)
4) (x+4)3
5) (2x-1)3
1.\(\left(x+5\right)^2=x^2+10x+25\)
2. \(\left(2x-5y\right)^2=4x^2-20xy+25y^2\)
3. \(\left(x+8\right)\left(x-8\right)=x^2-64\)
4. \(\left(x+4\right)^3=x^3+12x^2+48x+64\)
5. \(\left(2x-1\right)^3=8x^3-12x^2+6x-1\)
Đặt tính rồi tính:
34 x 2 23 x 3 22 x 4 11 x 5
bài 1:
a. S2 = 21+23+25+...+1001
b. S4 = 15+25+35+..+115
bài 2:
a. 2x-138= 23 .32
b. 5.(x+35) = 515
c. 814- ( x-305)=712
d. 20 - [ 7(x-3) +4] =2
e. 9x-1 =9
e. 5x-2 -32 = 24 - (28. 22 - 210 . 22)
Bài 1
S₂ = 21 + 23 + 25 + ... + 1001
Số số hạng của S₂:
(1001 - 21) : 2 + 1 = 491
⇒ S₂ = (1001 + 21) . 491 : 2 = 250901
--------
S₄ = 15 + 25 + 35 + ... + 115
Số số hạng của S₄:
(115 - 15) : 10 + 1 = 11
⇒ S₄ = (115 + 15) . 11 : 2 = 715
Bài 2
a) 2x - 138 = 2³.3²
2x - 138 = 8.9
2x - 138 = 72
2x = 72 + 138
2x = 210
x = 210 : 2
x = 105
b) 5.(x + 35) = 515
x + 35 = 515 : 5
x + 35 = 103
x = 103 - 35
x = 78
c) 814 - (x - 305) = 712
x - 305 = 814 - 712
x - 305 = 102
x = 102 + 305
x = 407
d) 20 - [7.(x - 3) + 4] = 2
7(x - 3) + 4 = 20 - 2
7(x - 3) + 4 = 18
7(x - 3) = 18 - 4
7(x - 3) = 14
x - 3 = 14 : 7
x - 3 = 2
x = 2 + 3
x = 5
e) 9ˣ⁻¹ = 9
x - 1 = 1
x = 1 + 1
x = 2
2:
a: \(2x-138=2^3\cdot3^2\)
=>\(2x-138=8\cdot9=72\)
=>2x=138+72=210
=>x=105
b: \(5\cdot\left(x+35\right)=515\)
=>x+35=103
=>x=103-35=68
c: \(814-\left(x-305\right)=712\)
=>x-305=814-712=102
=>x=102+305=407
d: \(20-\left[7\left(x-3\right)+4\right]=2\)
=>7(x-3)+4=18
=>7(x-3)=14
=>x-3=2
=>x=5
e: \(9^{x-1}=9\)
=>x-1=1
=>x=2
f: \(5^{x-2}-3^2=2^4-\left(2^8\cdot2^2-2^{10}\cdot2^2\right)\)
=>\(5^{x-2}-9=16-1024+4096\)
=>\(5^{x-2}=3097\)
=>\(x-2=log_53097\)
=>\(x=2+log_53097\)
Trong các phân số \(\dfrac{5}{4}\);\(\dfrac{22}{23}\);\(\dfrac{9}{9}\);\(\dfrac{24}{23}\) phân số bé nhất là
A.\(\dfrac{24}{23}\) B.\(\dfrac{22}{23}\) C.\(\dfrac{5}{4}\) D.\(\dfrac{9}{9}\)
`=>` `B`
Vì các phân số cồn lại thuộc dạng `(x >= 1)`
Bài 19 Rút gọn
1) (x+2)^2+(3-x)^2
2) (4-x)^2 -(x-3)^2
3) (x-5)(x+5)-(x+5)^2
4) (x-3)^2-(x-4)(x+4)
5) (y^2 -6y+9)-(3-y)^2
6. (2x+3)² –(2x–3).(2x+3)
1) Ta có: \(\left(x+2\right)^2+\left(x-3\right)^2\)
\(=x^2+4x+4+x^2-6x+9\)
\(=2x^2-2x+13\)
2) Ta có: \(\left(4-x\right)^2-\left(x-3\right)^2\)
\(=\left(4-x-x+3\right)\left(4-x+x-3\right)\)
\(=-2x+7\)
3) Ta có: \(\left(x-5\right)\left(x+5\right)-\left(x+5\right)^2\)
\(=x^2-25-x^2-10x-25\)
=-10x-50
4) Ta có: \(\left(x-3\right)^2-\left(x-4\right)\left(x+4\right)\)
\(=x^2-6x+9-x^2+16\)
=-6x+25
5) Ta có: \(\left(y^2-6y+9\right)-\left(y-3\right)^2\)
\(=y^2-6y+9-y^2+6y-9\)
=0
6) Ta có: \(\left(2x+3\right)^2-\left(2x-3\right)\left(2x+3\right)\)
\(=4x^2+12x+9-4x^2+9\)
=12x+18
Thực hiện phép tính: a) (-23).3; b) (-14).5; c) 22.(-3); d) 16.(-4)Thực hiện phép tính: a) (-23).3; b) (-14).5; c) 22.(-3); d) 16.(-4)
Bài 19 rút gọn
1) (x+2)^2+(3-x)^2
2) (4-x)^2-(x-3)^2
3) (x-5)(x+5)-(x+5)^2
4)(x-3)^2-(x-4)(x+4)
5) (y^2-6y+9)-(3-y)^2
6) (2x+3)^2-(2x-3)(2x+3)
1) Ta có: \(\left(x+2\right)^2+\left(x-3\right)^2\)
\(=x^2+4x+4+x^2-6x+9\)
\(=2x^2-2x+13\)
2) Ta có: \(\left(4-x\right)^2-\left(x-3\right)^2\)
\(=\left(4-x-x+3\right)\left(4-x+x-3\right)\)
\(=\left(-2x+7\right)\cdot1\)
\(=-2x+7\)
3) Ta có: \(\left(x-5\right)\left(x+5\right)-\left(x+5\right)^2\)
\(=x^2-25-x^2-10x-25\)
\(=-10x-50\)
Tìm x ϵ N biết :
a) 280 – ( x – 140 ) : 35 = 270 ;
b)( 190 – 2x ) : 35 – 32 = 16;
c) 720 : [ 41 – ( 2x – 5 ) ] = 23 .5
d) ( x : 23 + 45 ) . 37 – 22 = 24 . 105 ;
e) ( 3x – 4 ) . ( x – 1 ) 3 = 0 ;
f) 22x-1 : 4 = 83
g) x17 = x ;
h) ( x – 5 ) 4 = ( x – 5 ) 6 ;
i) ( x + 2 ) 5 = 210 ;
k ) 1 + 2 + 3 + … + x = 78
l) ( 3 .x – 24) . 73 = 2 .74 ;
n) 5x : 52 = 125 ;
m) ( x + 1) 2 = ( x + 1) 0 ;
o) ( 2 + x ) + ( 4 + x ) + ( 6 + x ) + ……+ ( 52 + x ) = 780 ;
p) 70⋮ x , 80 ⋮ x và x > 8
q) x ⋮ 12 , x ⋮ 25 , x ⋮ 30 và 0 < x < 500
4, -5/6 - 26/5 . 1/13
5, (19/23 - 22/46) . 23/16
6, (3/4 . - 5/7) . (20/9 . - 14/15)