Question

Nếu b=a-1 thì (a+b)(a^2+b^2)(a^4+b^4)...(a^32+b^32)=a^64+b^64

Ai làm đk thì giúp mik vs nhé!Thank nhìu

Answer 1

Có: \(b=a-1\Rightarrow a-b=1\)

\(\left(a+b\right)\left(a^2+b^2\right)\left(a^4+b^4\right)...\left(a^{32}+b^{32}\right)\)

\(=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)\left(a^4+b^4\right)...\left(a^{32}+b^{32}\right)\)

\(=\left(a^2-b^2\right)\left(a^2+b^2\right)\left(a^4+b^4\right)...\left(a^{32}+b^{32}\right)\)

\(=\left(a^{32}-b^{32}\right)\left(a^{32}+b^{32}\right)=a^{64}-b^{64}\)