In triangle ABC, the point X divides BC internally in the ration m:n, where m+n = 1. Express (AX)^2 in terms of AB , BC,CA,m and n.

My attempt :

(AX)^2 = (AB)^2 - (BX)^2 ----1

(AX)^2 = (CA)^2 - (XC)^2 ----2

1+2 , 2(AX)^2 = (AB)^2 + (CA)^2 - (m BC)^2 - (n BC)^2

(AX)^2 = [(AB)^2 +(CA)^2 - (m BC)^2 - (n BC)^2]/2