Question

Viết gọn biểu thức sau dưới dạng 1 phân thức:A=(x²-x+1)(x⁴-x²+1)(x⁸-x⁴+1)(x¹⁶-x⁸+1)(x³²-x¹⁶+1)[giải thích hộ mình nữa nhé]

Answer 1

\(A\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)...\left(x^{32}-x^{16}+1\right)\)

\(A\left(x^2+x+1\right)=\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)...\left(x^{32}-x^{16}+1\right)\)

(Giải thích: \(\left(x^2+x+1\right)\left(x^2-x+1\right)=\left(x^2+1\right)^2-x^2=x^4+x^2+1\))

\(A\left(x^2+x+1\right)=\left(x^8+x^4+1\right)\left(x^8-x^4+1\right)...\left(x^{32}-x^{16}+1\right)\)

.....

\(A\left(x^2+x+1\right)=x^{64}-x^{32}+1\)

\(\Rightarrow A=\frac{x^{64}-x^{32}+1}{x^2+x+1}\)