设原式中的两数是a,b,令x=a-b, 得(a-b)^3=a^3-b^3-3ab(a-b), 得x^3=14-3x,即x^3+3x-14=0, 即(x-2)(x^2+2x+7)=0, 所以x=2是唯一的实数根,即原数=2, 是有理数。
设原式中的两数是a,b,令x=a-b, 得(a-b)^3=a^3-b^3-3ab(a-b), 得x^3=14-3x,即x^3+3x-14=0, 即(x-2)(x^2+2x+7)=0, 所以x=2是唯一的实数根,即原数=2, 是有理数。
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