若M=(x^a+2x^2+1)(x^4-2x^2+1),N=(x^4+x^2+1)(x^4-x^2+1)试比较M与N的大

duan89522022-10-04 11:39:541条回答

若M=(x^a+2x^2+1)(x^4-2x^2+1),N=(x^4+x^2+1)(x^4-x^2+1)试比较M与N的大小

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nj1932 共回答了20个问题 | 采纳率85%: ∵ M=(x^4+2x^2+1)(x^4-2x^2+1),N=(x^4+x^2+1)(x^4-x^2+1) ∴ M/N=[(x^4+2x^2+1)(x^4-2x^2+1)] / [(x^4+x^2+1)(x^4-x^2+1)] ={(x^4+x^2+1)(x^2-1)^2 + [X(X^2-1)]^2 } / [(x^4+x^2+1)(x^4-x^2+1)] =(x^4+x^2+1)(x^2-1)^2 / [(x^4+x^2+1)(x^4-x^2+1)] + [X(X^2-1)]^2 / [(x^4+x^2+1)(x^4-x^2+1)] >(x^4+x^2+1)(x^2-1)^2 / [(x^4+x^2+1)(x^4-x^2+1)] =(x^2-1)^2 / (x^4-x^2+1) =1 - x^2 / (x^4-x^2+1) >1 ∴ M > N; 1年前