Question

已知x=根号3-根号2分之根号3+根号2,y=根号3+根号2分之根号3-根号2,求y分之x+x分之y

Answer 1

分母有理化：x=(√3－√2)²=5-2√6 y=(√3＋√2)²=5－2√6
x＋y=10 xy=1
x/y+y/x=(x+y)²-2xy=10²-2=98

Answer 2

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

y/x+x/y=(y^2+x^2)/xy=(x+y)^2-2xy
=[(√3+√2)^2+(√3-√2)^2]^2-2
=10^2-2
=98

Answer 3

x=(√3+√2)/(√3-2)
=(√3+√2)(√3+√2)/(√3-2)(√3+√2)
=(5+2√6)
y=(√3+√2)/(√3+2)
=(√3-√2)(√3-√2)/(√3+2)(√3-√2)
=(5-2√6)
x/y+y/x
=(5-2√6)/(5+2√6)+(5+2√6)/(5-2√6)
=(49-20√6)+(49+20√6)
=98