X+6=Y 3*(1/X+1/Y)+1/Y=1

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X+6=Y 3*(1/X+1/Y)+1/Y=1
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X+6=Y 3*(1/X+1/Y)+1/Y=1
X+6=Y 3*(1/X+1/Y)+1/Y=1

X+6=Y 3*(1/X+1/Y)+1/Y=1
3/x+4/y=1
3/x+4/(x+6)=1
3x+18+4x=x²+6x
x²-x-18=0
x=(1±√73)/2
y=x+6
所以
x=(1-√73)/2,y=(13-√73)/2
x=(1+√73)/2,y=(13+√73)/2

解方程组：
x+6=y....................(1)
3/x+4/y=1..............(2）
将（1）代入（2）得
3/x+4/(x+6)=1
去分母得 3(x+6)+4x=x(x+6)
化简得x²-x-18=0
故x=(1±√73)/2，y=(1±√73)/2+6=(12±√73)/2.(x与y的根号前同取正号或负号）

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