Question

Докажите неравенство:a) (а-1)(а+1)(a^2+1)(a^4+1)(a^8+1)=a^16-1
б) (b+c)(b^2+c^2)(b^4+c^4)(b^8+c^8)= (b^16-c^16)/b-c ( b не равно c)

Answer 1

а) a^16 -1=(a^8)^2 - 1^2=(a^8 +1)(a^8 - 1)=(a^8 +1)(a^4 + 1)(a^4-1)=
=(a^8+1)(a^4+1)(a^4-1) =(a^8+1)(a^4+1)(a2+1)(a^2 -1)=
=(a^8+1)(a^4+1)(a^2+1)(a+1)(a-1).

б) (b^16 - c^16) / (b -c) =(b^8+c^8)(b^8 - c^8) /(b - c)=
= (b^8+c^8)(b^4+c^4)(b^4 - c^4) / (b - c) =
=(b^8+c^8)(b^4+c^4)(b^2+c^2)(b^2-c^2) / (b - c) =
=(d^8+c^8)(v^4+c^4)(b^2+c^2((b+c)(b-c) / (b - c) =
=(b^8+c^8)(b^4+c^4)(b^2+c^2((b+c)