先化简再求植:0.5(x+y+2)＾+0.5(x-y-2)(x-y+2)-2(x+y)其中x-y=6,xy=21
问题描述：
先化简再求植:0.5(x+y+2)＾+0.5(x-y-2)(x-y+2)-2(x+y)其中x-y=6,xy=21
答
因为x-y=6,xy=21
(x+y)^2=(x-y)^2+4xy=36+84=100
x+y=10或x+y=-10
先设x+y=10
原式=0.5*144+0.5*4*8-2*10=72+16-20=68
再设x+y=-10
原式=0.5*64+0.5*4*8-2*(-10)=32+16+20=68
所以两种解都是68
答
思路:
0.5(x+y+z)方+0.5(x-y-z)(x-y+z)-2(x+y)
=0.5[(x+y)方+2z(x+y)+z方]+0.5[(x-y)方-z方]-z(x+y)
=0.5(x+y)方+0.5(x-y)方=x方＋y方
由x-y=6,xy=21得,
x方＋y方＝（x-y）方＋2xy＝78
注:y方是y的平方.