2016/057)If a,b,c and d are in G.P then show that $(b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2$

a,b,c,d are in GP let common ratio be x $b = ax,c = ax^2,, d = ax^3$ LHS = $(ax-ax^2)^2 + (ax^2-a)^2 + (ax^3- ax)^2$ $= a^2(x^2 (1-x)^2) + (x^2-1)^2 + x^2(x^2-1)^2)$ $= a^2(x^2(1-2x+x^4) + ( 1- 2x^2 + x^ 4) + x^2(x^4-2x^2+ 1)$ $= a^2(1- 2x^3+x^6)$ $= a^2(1-x^3)^2$ $= ( a- (ax^3))^2$ $= (a-d)^2$