Có: (x - 1)³ = 7³

=> x - 1 = 7

x = 7 + 1

x = 8

ab(a+b) - bc(b + c) + ac(a - c)

=a²b + ab² - b²c - bc² + a²c - ac²

=(ab² - b²c) + (a²c - ac²) + (a²b - bc²)

=b²(a - c) + ac(a - c) + b(a² - c²)

=b²(a - c) + ac(a - c) + b(a - c)(a + c)

=(a - c )[b² + ac + b(a + c)]

=(a - c)[(b² + bc) + (ab + ac)]

=(a - c)[b(b + c) + a(b + c)]

=(a - c)(a + b)(b + c)

a) x⁴ + 2x³ + 2x² + 2x + 1

=[ (x²)² + 2.x².x + x² ] + (x² + 2.x.1 + 1²)

=(x² + x)² + (x + 1)²

=[x(x + 1)]² + (x + 1)²

=x²(x + 1)² + (x + 1)²

=(x² + 1)(x + 1)²

b) x² - 2x - 4y² - 4y

= [x² - (2y)²] - 2(x - 2y)

= (x - 2y)(x + 2y) - 2(x - 2y)

= (x + 2y - 2)(x - 2y)

a) 17.13+17.42-17.35

=17.(13+42-35)

=17.20=340

b) [25.(18-4²)-10]:4+6

=(25.2-10):4+6

=40:4+6=16

c) 3⁶:3²+2³.2²-3².3

=3⁴+2⁵-3³

=81+32-27=86

d) B=3.4²-2².3

=3.(16-4)

=3.12=36

e)2022⁰+3.[5².10-(23-13)²]

=1+3.(250-100)

=1+450=451

g) 27.77+24.27-27

=27.(77+24-1)

=27.100=2700

h) 5.2³+7⁹:7⁷-1²⁰²⁰

=40+7²-1

=89-1=88

i) 120:{54[50:2+(3²-2.4)]}

=120:[54(25+1)]

=120:1404=10/117

a) \(\left(\dfrac{3}{5}-\dfrac{1}{2}\right)^2=\left(\dfrac{1}{10}\right)^2=\dfrac{1}{100}.\)

b) \(\left(0,5+1\dfrac{1}{2}\right)^3=2^3=8.\)

a) 0,25=(0,5)²;  \(\dfrac{8}{125}=\left(\dfrac{2}{5}\right)^3\)

\(-\dfrac{27}{125}=\left(-\dfrac{3}{5}\right)^3\); \(\dfrac{121}{169}=\left(\dfrac{11}{13}\right)^2\)

b) \(\left(\dfrac{1}{4}\right)^3=\left[\left(\dfrac{1}{2}\right)^2\right]^3=\left(\dfrac{1}{2}\right)^6\);

\(\left(\dfrac{1}{8}\right)^5=\left[\left(\dfrac{1}{2}\right)^3\right]^5=\left(\dfrac{1}{2}\right)^{15}\)

\

(1/2+x) (2x-3)=0

=> 1/2+x=0 hoặc 2x-3=0

x=-1/2 hoặc x=3/2

1/27-(x+1/2)³=0

=> (x+1/2)³=1/27

=> x+1/2=1/3

=> x=-1/6

Số các số hạng trong S là: (2023-4):3+1=674 (số)

Tổng S bằng: (2023+4).674:2=683099

Vậy S=683099