Question

若x=123456789×123456786，Y=123456788×123456787，试比较x,y大小，解：设123456788=a,

那么x=（a+1）(a-2)=a²-a-2，y=a(a-1)=a²-a∵x-y=（a²-a-2）-(a²-a)=-2＜0∴x＜y，请用这个方法算出1.345×0.345×2.69-1.345³-1.345×0.345²
快，好的给分

Answer 1

x=1.345×0.345×2.69 y=1.345³-1.345×0.345²
设a=0.345
x=(a+1)×a×2(1+a)
=2a(a+1)²
y=(1+a)³-(1+a)×a²
=(a+1)[(a+1)²-a²]
=(a+1)(2a+1)
x-y=2a(a+1)²-(a+1)(2a+1)
=(a+1)[2a(a+1)-(2a+1)]
=(a+1)(2a²-1)
∵(a+1)＞0 (2a²-1)＜0
∴(a+1)(2a²-1)＜0
x-y＜0
x＜y
∴1.345×0.345×2.69-1.345³-1.345×0.345²＜0

追问

是计算

追答

x-y=2a(a+1)²-(a+1)(2a+1)
=(a+1)[2a(a+1)-(2a+1)]
=(a+1)(2a²-1)
带入a=0.345就是了

Answer 2

本题中0.345和2.69都与1.345有关系，可设1.345=x，那么0.345=x-1，2.69=2x，然后进行计算．解：设1.345=x，原式=x（x-1）•2x-x3-x（x-1）2，
=（2x3-2x2）-x3-x（x2-2x+1），
=2x3-2x2-x3-x3+2x2-x，
=-1.345．

Answer 3

x=a(a-2)=a的平方-2a,y=a(a-1)=a的平方-2a+1=x+1，所以，x小于y

Answer 4

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