Question

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

Answer 1

∵ 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