已知x=根号下2+1/根号下2-1,y=根号下2-1/根号下2+1,求下列各式的值.（1）y/x+x/y
问题描述：
已知x=根号下2+1/根号下2-1,y=根号下2-1/根号下2+1,求下列各式的值.（1）y/x+x/y
答
XY=1
就是(X^2+Y^2)/(XY)=(X+Y)^2-2XY=( (√2+1)^2+(√2-1/)^2 )^2 - 2=(3+3)^2-2=34
答
解
是x=√2+1/(√2-1)吗?
xy=(√2+1)/(√2-1)×(√2-1)/(√2+1)=1
x²+y²=(√2+1)²/(√2-1)²+(√2-1)²/(√2+1)²
=(3+2√2)/(3-2√2)+(3-2√2)/(3+2√2)
=[(3+2√2)²-(3-2√2)²]/(3-2√2)(3+2√2)
=(12√2+12√2)/(9-8)
=24√2
y/x+x/y
=(y²+x²)/xy
=24√2