已知X=根号2+1分之根号2-1,Y=根号2-1分之根号2+1,求代数式X^2-XY+ Y^2的值.

问题描述:

已知X=根号2+1分之根号2-1,Y=根号2-1分之根号2+1,求代数式X^2-XY+ Y^2的值.

X=根号2+1分之根号2-1,Y=根号2-1分之根号2+1
X^2=(根号2-1)^2=3-2根号2
XY=1
Y^2=(根号2+1)^2=3+2根号2
X^2-XY+ Y^2=3-2根号2-1+3+2根号2=5