х-1=(корень изх+1)*(корень изх-1)
(a-x)(x³-y³)-(x-y)(a³-x³)=
=(a-x)(x-y)(x²+xy+y²)-(x-y)(a-x)(a²+ax+x²)=
=(a-x)(x-y)(x²+xy+y²-a²-ax-x²)=
=(a-x)(x-y)(y²-a²+xy-ax)
2x³-2xy²-6x²+6y²=
=(2x³-2xy²)-(6x²-6y²)=
=2x(x²-y²)-6(x²-y²)=
=(x²-y²)(2x-6)=
=2(x-3)(x-y)(x+y)
5a²-5b²-10a³b+10ab³=
=(5a²-5b²)-(10a³b-10ab³)=
=5(a²-b²)-10ab(a²-b²)=
=(a²-b²)(5-10ab)=
=5(1-5ab)(a-b)(a+b)
36x³-144x-36x²+144=
=(36x³-36x²)-(144x-144)=
=36x²(x-1)-144(x-1)=
=(x-1)(36x²-144)=
=(x-1)(6x-12)(6x+12)=
=(x-1)*6(x-2)*6(x+2)=
=36(x-1)(x-2)(x+2)
y³+ay²-b²y-b²a=
=(y³+ay²)-(b²y+b²a)=
=y²(y+a)-b²(y+a)=
=(y+a)(y²-b²)=
=(y+a)(y-b)(y+b)
2,32(4) = 2,32 + 0,00(4)
0,00(4) = 0,004 + 0,0004 + 0,00004 +... - сумма бесконечно убывающей геометрической прогрессии
b₁ = 0,004
b₂ = 0,0004
q = b₂/b₁ = 0,0004/0,004 = 0,1
S = b₁/(1 - q) = 0,004/(1 - 0,1) = 0,004/0,9 = 4/900 = 1/225
2,32 + 1/225 = 232/100 + 1/225 = 58/25 + 1/225 = 522/225 + 1/225 = 523/225
Ответ: 2,32(4) = 523/225.
0,(47) = 0,47 + 0,0047 + 0,000047 + ... - сумма бесконечно убывающей геометрической прогрессии
b₁ = 0,47
b₂ = 0,0047
q = b₂/b₁ = 0,0047/0,47 = 0,01
S = b₁/(1 - q) = 0,47/(1 - 0,01) = 0,47/0,99 = 47/99
Ответ: 0,(47) = 47/99.