Question

已知x平方+根号2乘以y（根号内是2）=根号3,y方+根号2乘以x（根号内是2）=根号3,且x不等于y,求y/x+x/y

Answer 1

x^2+√2y=√3

y^2+√2x=√3

两式相减

x^2-y^2+√2y-√2x=0

(x-y）(x+y)-√2(x-y)=0

(x-y)(x+y-√2)=0

x不等于y

x+y-√2=0

x+y=√2

x^2+√2y=√3

y^2+√2x=√3

两式相加

x^2+y^2+√2(x+y)=2√3

x^2+y^2+2=2√3

x^2+y^2=2√3-2

(x+y)^2=x^2+2xy+y^2=2

2xy=2-x^2-y^2=2-(2√3-2)=4-2√3

xy=2-√3

y/x+x/y=(x^2+y^2)/xy=（2√3-2）/(2-√3)=4√2+2√6-2√3-4