CDS Model Paper 2 Mathematics

x(x+a)(x+2a)(x+3a)
=(x2+ax)(x2+5ax+6a2)
=x4+ax3+5ax3+5a2x2+6a2x2+6a3x
=x4+ax(x2+5x2+5ax+6ax+6a2)
So, for terms to be perfect square,
=(x+y)2(x+y)2=(x2+2xy+y2)(x2+y2+2xy)
=x4+2x3y+x2y2+x2y2+2xy3+y4+2x3y+4x2y2+2xy3
=x4+xy(4x2+6xy+4y2)+y4 ...(ii)
On comparing equations. (i) and (ii), as y=a
a4 must be added to make it a perfect square.
Let x=1 and a=1 solve
1(2)(3)(4)=24
1 need to complete square
∴ a4=14=1