Question

已知a是实数,A=(a^2)/(a^4+1),B=(a^4)/(a^6+1),比较A与B的大小

Answer 1

A-B

=a^2/(a^4+1)-a^4/(a^6+1)

=[a^2(a^6+1)-a^4(a^4+1)]/[(a^4+1)(a^6+1)]

=(a^8+a^2-a^8-a^4)/[(a^4+1)(a^6+1)]

=-a^2(a^2-1)/[(a^4+1)(a^6+1)]

a=0或a=1或a=-1时,A-B=0 A=B

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