已知:x*x+√3y=√5,y*y+√3x=√5,且x≠y,求 y/x+x/y
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已知:x*x+√3y=√5,y*y+√3x=√5,且x≠y,求 y/x+x/y
x*x+√3y=√5,y*y+√3x=√5
x*x+√3y=y*y+√3x
x*x+√3y-y*y-√3x=0
(x-y)(x+y)-√3(x-y)=0
(x-y)(x+y-√3)=0
x≠y,x-y≠0
x+y-√3=0
x+y=√3
(x+y)*(x+y)=3
x*x+2xy+y*y=3 x*x+y*y=3-2xy
x*x+√3y=√5,y*y+√3x=√5
x*x+√3y+y*y+√3x=x*x+y*y+√3(x+y)=2√5
3-2xy+√3*√3=2√5
2xy=6-2√5
xy=3-√5
x*x+y*y=3-2xy=2√5-3
y/x+x/y=(x*x+y*y)/xy=(2√5-3)/(3-√5)=(1+3√5)/4
x*x+√3y=y*y+√3x
x*x+√3y-y*y-√3x=0
(x-y)(x+y)-√3(x-y)=0
(x-y)(x+y-√3)=0
x≠y,x-y≠0
x+y-√3=0
x+y=√3
(x+y)*(x+y)=3
x*x+2xy+y*y=3 x*x+y*y=3-2xy
x*x+√3y=√5,y*y+√3x=√5
x*x+√3y+y*y+√3x=x*x+y*y+√3(x+y)=2√5
3-2xy+√3*√3=2√5
2xy=6-2√5
xy=3-√5
x*x+y*y=3-2xy=2√5-3
y/x+x/y=(x*x+y*y)/xy=(2√5-3)/(3-√5)=(1+3√5)/4
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