Question

Упростите и вычислите

(2^(2)+1)×(2^(4)+1)×(2^(8)+1)
×(2^(16)+1)×(2^(32)+1)
×(2^(64)+1)−(1/3)×2^(128)​

Answer 1

Ответ:

-1

Пошаговое объяснение:

(2^2 +1)(2^4 +1)(2^8 +1)(2^16 +1)(2^32 +1)(2^64 +1) -1/3 •2^128=(2^2 -1)(2^2 +1)(2^4 +1)(2^8 +1)(2^16 +1)(2^32 +1)(2^64 +1) -1/3 •2^128 •(2^2 -1)=-1

По дейсвиям:

(2^2 -1)(2^2 +1)=2^4 -1

(2^4 -1)(2^4 +1)=2^8 -1

(2^8 -1)(2^8 +1)=2^16 -1

(2^16 -1)(2^16 +1)=2^32 -1

(2^32 -1)(2^32 +1)=2^64 -1

(2^64 -1)(2^64 +1)=2^128 -1

2^128 -1 -1/3 •2^128 •(2^2 -1)=2^128 -1 -1/3 •2^128 •3=2^128 -1-1•2^128=2^128-1-2^128=-1