(1) Calculate 1×2≠2×( 1+2), 4×4=2×(4+4).

(2) when a > 0, calculate a according to (a+3)×2=3a, and further calculate b; When a < 0, calculate a according to (-a+3)×2=-3a, and then calculate B. 。

Answer:

Solution:

( 1)

∵ 1×2≠2×( 1+2),4×4=2×(4+4),

Point M is not harmonious point, and point N is harmonious point.

(2) From the meaning of the question: when a > 0, (a+3)×2=3a,

∴a=6，

Point P(a, 3) is on the straight line y=-x+b, and b=9.

When a < 0, (-a+3)×2=-3a,

∴a=-6，

Point P(a, 3) is on the straight line y=-x+b, and b=-3.

∴a=6, b=9 or a=-6, B =-3.