Question

已知x=√2-1，y=√2+1 求下列各式的值.

1. x²-y²
2. y/x+x/y

Answer 1

1、原式=(x+y)(x-y)=(√2-1+√2+1)(√2-1-√2-1)=-4√2
2、原式=(x^2+y^2)/(xy)=[(x+y)^2-2xy]/xy=(x+y)^2/xy-2=(√2-1+√2+1)^2/(√2-1)(√2+1)-2=8

Answer 2

x²-y²=（x+y)(x-y)=2√2*(-2)=-4√2；

y/x+x/y=y^2/xy+x^2/xy=(x^2+y^2)/xy=(3-2√2+3+2√2)/1=6

Answer 3

1、原式=(x+y)(x-y)=(√2-1+√2+1)(√2-1-√2-1)=-4√2
2、原式=(x^2+y^2)/(xy)=[(x+y)^2-2xy]/xy=(x+y)^2/xy-2=(√2-1+√2+1)^2/(√2-1)(√2+1)-2=8