设x=3+√6cosa,A=y/x,则y=3+√6sina
于是,A=(3+√6sina)/(3+√6cosa)
==>(3+√6cosa)A=3+√6sina
==>Acosa-sina=3(1-A)/√6
==>[A/√(A²+1)]cosa-[1/√(A²+1)]sina=3(1-A)/√[6(A²+1)].(1)
令 A/√(A²+1)=cosb,则 1/√(A²+1)=sinb
代入(1)得cosacosb-sinasinb=3(1-A)/√[6(A²+1)]
==>cos(a+b)=3(1-A)/√[6(A²+1)]
∵ │cos(a+b)│≤1
==>│3(1-A)/√[6(A²+1)]│≤1
==>3│1-A│≤√[6(A²+1)]
==>A-6A+1≤0
==>3-2√2≤ A ≤3+2√2
∴y/x的最大值是3+2√2,最小值是3-2√2.