Bài 1: 

a) 0²⁰⁰² < 0²⁰²³

b) 2022⁰ = 2023⁰

c) 54⁹ < 55¹⁰

d) ( 4 + 5 )³ > 4² + 5²

đ) 9² - 3² > ( 9 - 3 )²

Bài 2:

a) 3² x 4³ - 3² + 333

= 9 x 64 - 9 + 333

= 576 - 9 + 333

= 567 + 333

= 900

b) 5 x 4³ + 24 x 5 + 41⁰

= 5 x 64 + 24 x 5 + 1

= 5 x ( 64 + 24 ) + 1

= 5 x 88 + 1

= 440 + 1

= 441

c) 2³ x 4² + 3² x 5 - 40 x 1²⁰²³

= 8 x 16 + 9 x 5 - 40 x 1

= 128 + 45 - 40

= 133

Bài 1 :

a) \(0^{2002}=0;0^{2023}=0\Rightarrow0^{2002}=0^{2023}\)

b) \(2022^0=1;2023^0=1\Rightarrow2022^0=2023^0\)

c) \(54^9< 55^9;55^9< 55^{10}\Rightarrow54^9< 55^{10}\)

d) \(\left(4+5\right)^3>\left(4+5\right)^2;\left(4+5\right)^2>4^2+5^2\Rightarrow\left(4+5\right)^3>4^2+5^2\)

đ) \(9^2-3^2=81-9=82;\left(9-3\right)^2=6^2=36\Rightarrow9^2-3^2>\left(9-3\right)^2\)

Bài 2 :

a) \(3^2.4^3-3^2+333=3^2\left(4^3-1\right)+9.37=9.63+9.37=9\left(63+37\right)=9.100=900\)

b) \(5.4^3+24.5+41^0=20.4^2+20.6+1=20\left(16+6\right)+1=20.22+1=441\)

c) \(2^3.4^2+3^2.5-40.1^{2023}=8.16+9.5-40.1=128+45-40=128+5=133\)

Lời giải:
a. $x^3=4^3\Rightarrow x=4$

b. $x^2=49=7^2=(-7)^2$

$\Rightarrow x=7$ hoặc $x=-7$

c. $x^3+1=28$

$x^3=28-1=27=3^3$

$\Rightarrow x=3$

d. $2^x=16=2^4$

$\Rightarrow x=4$

e. $2^4.2^x=2^6$

$\Rightarrow 2^{4+x}=2^6$

$\Rightarrow 4+x=6$

$\Rightarrow x=2$

g.

$5^x=25.5^3=5^2.5^3=5^5$

$\Rightarrow x=5$

Lần sau bạn lưu ý viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để đề được rõ ràng hơn nhé.

a. x mũ 2 - 2x + 1 = 25 

= x^2 + 2.x.1 + 1^2

= ( x + 1 ) ^2

ko bt có đúng ko nữa, mấy câu kia tui ko bt lm

Sos

hahaha

\(a.x-143=57\)

\(x=200\)

\(b.\left(8x-12\right):4=3^3\)

\(8x-12=27.4\)

\(8x-12=108\)

\(8x=120\)

\(x=15\)

\(d.10+2x=4^2\)

\(2x=16-10\)

\(2x=6\)

\(x=3\)

a) 716-(x-143)=659

<=>x-143=57

<=>x=57+143

<=>x=200

b) [(8x-12):4].3³=3⁶

<=>(8x-12):4=3³

<=>8x-12=27.4

<=>8x-12=108

<=>8x=120

<=>x=5

c) -2<|x|≤1, x thuộc Z

Vì -2<|x|≤1

=>|x| thuộc {-1;0;1}

+)Với |x|=-1=>Vô lí

+)Với |x|=0=>x=0(tm)

+)Với |x|=1=>x=-1;1(tm) 

Vậy x thuộc {-1;1;0}

d) 10+2x=4⁵:4³

<=>10+2x=16

<=>2x=6

<=>x=3

e) 4^x+1+4⁰=65

<=>4^x+1+1=65

<=>4^x+1=64

<=>4^x+1=4³

<=>x+1=3

<=>x=2

g) 96-2(x+1)=-42

<=>2(x+1)=96+42

<=>2(x+1)=138

<=>x+1=69

<=>x=68

h) 4x-20=2⁵:2²

<=>4x-20=2³

<=>4x=8+20

<=>4x=28

<=>x=7

k) 8x-75=5x+21

<=>8x-5x=75+21

<=>3x=96

<=>x=32

i) [(8x-14):2-2].31=341

<=>(8x-14):2-2=11

<=>(8x-14):2=13

<=>8x-14=26

<=>8x=40

<=>x=5

a)64:2mũ5×30×4

= 64 : 32 x 30 x 4

= 240

b)3 mũ 2× 5 - 2 mũ 2×7+2 mũ 0 × 5

= 9 x 5 - 4 x 7 + 1 x 5

= 45 - 28 + 5

= 22

c)2 mũ 3-5 mũ 3÷5 mũ 2 + 12×2 mũ 2

= 8 - 125 : 25 + 12 x 4

= 8 - 5 + 48

= 51

d)2[(7-3 mũ 3÷3 mũ 2) chia 2 mũ 2 + 99]-100

= 2[( 7 - 27 : 9) : 4 + 99] - 100

= 2[4 : 4 + 99] - 100

= 2. 100 - 100

= 200 - 100

= 100

e)4[(3 + 3^7:3^4)chia 10 + 97]-300

= 4[( 3 + 3^3) : 10 + 97] - 300

= 4[ 30 : 10 + 97 ] - 300

= 4. 100 - 300

= 400 - 300

= 100

f)2^2 x 5 [(5 mũ 2 cộng 2 mũ 3) chia 11 - 2] - 3^2 x 2

= 4 x 5 [ (25 + 8 ) : 11 - 2] - 9 x 2

= 20 [ 33 : 11 - 2] - 18

= 20. 1 - 18

= 20 - 18

= 2

hum biết nữa

a)240

b)22

c)51

d)100

e)100

f)2

a) 2( x - 1 )² - 4( 3 + x )² + 2x( x - 5 )

= 2( x² - 2x + 1 ) - 4( 9 + 6x + x² ) + 2x² - 10x

= 2x² - 4x + 2 - 36 - 24x - 4x² + 2x² - 10x

= ( 2x² - 4x² + 2x² ) + ( -4x - 24x - 10x ) + ( 2 - 36 )

= -38x - 34

b) 2( 2x + 5 )² - 3( 4x + 1 )( 1 - 4x )

= 2( 4x² + 20x + 25 ) + 3( 4x + 1 )( 4x - 1 )

= 8x² + 40x + 50 + 3( 16x² - 1 )

= 8x² + 40x + 50 + 48x² - 3

= 56x² + 40x + 47

c) ( x - 1 )³ - x( x - 3 )² + 1

= x³ - 3x² + 3x - 1 - x( x² - 6x + 9 ) + 1

= x³ - 3x² + 3x - x³ + 6x² - 9x

= 3x² - 6x

d) ( x + 2 )³ - x²( x + 6 ) 

= x³ + 6x² + 12x + 8 - x³ - 6x²

= 12x + 8

e) ( x - 2 )( x + 2 ) - ( x + 1 )³ - 2x( x - 1 )²

= x² - 4 - ( x³ + 3x² + 3x + 1 ) - 2x( x² - 2x + 1 )

= x² - 4 - x³ - 3x² - 3x - 1 - 2x³ + 4x² - 2x

= -3x³ + 2x² - 5x - 5 

f) ( a + b - c )² - ( b - c )² - 2a( b - c )

= [ ( a + b ) - c ]² - ( b² - 2bc + c² ) - 2ab + 2ac

= [ ( a + b )² - 2( a + b )c + c² ] - b² + 2bc - c² - 2ab + 2ac

= a² + 2ab + b² - 2ac - 2bc + c² - b² + 2bc - c² - 2ab + 2ac

= a²

a) \(2\left(x-1\right)^2-4\left(3+x\right)^2+2x\left(x-5\right)\)

Dùng hẳng đẳng thức thứ nhất + hai :

= \(2\left(x^2-2\cdot x\cdot1+1^2\right)-4\left(3^2+2\cdot3\cdot x+x^2\right)+2x^2-10x\)

= \(2\left(x^2-2x+1\right)-4\left(9+6x+x^2\right)+2x^2-10x\)

= \(2x^2-4x+2-36-24x-4x^2+2x^2-10x\)

= \(-38x-34\)

b) 2(2x + 5)² - 3(4x + 1)(1 - 4x)

Dùng đẳng thức thứ 1 + 3

= 2[(2x)² + 2.2x.5 + 5² ] - (-3)[(4x)² - 1² ]

= 2(4x² + 20x + 25) - (-3).(16x² - 1)

= 8x² + 40x + 50 - (3 - 48x²)

= 8x² + 40x + 50 - 3 + 48x²

= 56x² + 40x + 47

c) (x - 1)³ - x(x - 3)² + 1

Dùng đẳng thức 2 + 5:

= x³ - 3.x².1 + 3.x.1² - 1³ - x(x² - 2.x.3 + 3²) + 1

= x³ - 3x² + 3x - 1 - x³ + 6x² - 9x + 1

= (x³ - x³) + (-3x² + 6x²) + (3x - 9x) + (-1 + 1)

= 3x² - 6x

d) (x + 2)³ - x²(x + 6)

= x³ + 3.x².2 + 3.x.2² + 2³ - x³ - 6x²

= x³ + 6x² + 12x + 8 - x³ - 6x²

= (x³ - x³) + (6x² - 6x²) + 12x + 8 = 12x + 8

e) Dùng đẳng thức thứ 3,4 và 2

= x² - 4 - (x³ + 3.x².1 + 3.x.1² + 1³) - 2x(x² - 2.x.1 + 1²)

= x² - 4 - (x³ + 3x² + 3x + 1) - 2x³ + 4x² - 2x

= x² - 4 - x³ - 3x² - 3x - 1 - 2x³ + 4x² - 2x

= (x² - 3x² + 4x²) + (-4 - 1) + (-x³ - 2x³) + (-3x - 2x)

= 2x² - 5 - 3x³ - 5x

f) Đặt \(a+b-c=A\)

\(b-c=B\)

= \(A^2-B^2-2AB\)

= \(A^2-2AB+\left(-B\right)^2\)

\(=A^2-2AB+B^2\)

= (A - B)²

= (a + b - c - (b - c))²

= (a + b - c - b + c)²

= a²

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