∵实数x、y满足x²-2x+4y=5
∴y=

5−x2+2x

4

∴x+2y=x+2×

5−x2+2x

4

=-

1

2

x²+2x+

5

2

∴最大值为

4×(− 1 2 ) × 5 2 −22

4× (− 1 2 )

=

9

2

．