Let the linear equation be y = k(x- 1) and the ellipse be y 2 =1-x 2/2.

(k^2+ 1/2)x^2 -2k^2 x+k^2- 1 = 0

The x coordinates of a and b are obtained as follows.

Ax = (2k 2+radical symbol (4k4-4 (k2-1) (k2+1/2))/(2 (k2+1/2))

Bx = (2k^2？ -radical sign (4k4-4 (k2-1) (k2+1/2))/(2 (k2+1/2))

AM= 1/3 BM，AM = 1/2 BM

Ax - Mx = 1/2 (Mx - Bx)

ax- 1 = 1/2- 1/2 Bx

Ax + 1/2 Bx = 3/2

Get k = +/- radical sign (7/2)