已知x=1-根号2,y=根号2+1.求-x²+2xy-y²的值

问题描述:

已知x=1-根号2,y=根号2+1.求-x²+2xy-y²的值

x=1-√2,y=√2+1
∴x-y=1-√2-√2-1=-2√2.
-x²+2xy-y²=-(x²-2xy+y²)=-(x-y)²
=-(2√2)²=-8.
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