若a=2,求3(a²+1)(a四次方+1)(a八次方+1)(a十六次方+1)
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解
3(a²+1)(a^4+1)(a^8+1)(a^16+1)
=3(a²-1)(a²+1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^4-1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^8-1)(a^8+1)(a^16+1)/(a²-1)
=3(a^16-1)(a^16+1)/(a²-1)
=3(a^32-1)/(a²-1)
=3×(2^32-1)/(4-1)
=2^32-1
3(a²+1)(a^4+1)(a^8+1)(a^16+1)
=3(a²-1)(a²+1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^4-1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^8-1)(a^8+1)(a^16+1)/(a²-1)
=3(a^16-1)(a^16+1)/(a²-1)
=3(a^32-1)/(a²-1)
=3×(2^32-1)/(4-1)
=2^32-1
追问
3×(2^32-1)/(4-1)怎么得到2^32-1的？
追答
就是
将a=2代入
=3×(2^32-1)/(2²-1)
=3(2^32-1)/3
=2^32-1
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