y=2cos²x+sin2x
=1+cos2x+sin2x
=1+

2

(

2

2

cos2x+

2

2

sin2x)
=1+

2

sin(2x+

π

4

)
当 2x+

π

4

=2kπ+

π

2

，有最小值1+

2

故答案为：1+

2

．