If `A=2B`, then prove that either `c=b` or `a^2 = b(c+b)`

If a,b,c, are in AP,quad a^(2),b^(2),c^(2) are in HP ,then prove that either a=b=c or a,b,-(c)/(2) from a GP (2003,4M)

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

If a,b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P. then prove that either a^(2),b^(2),c^(2) are in H.P.a=b=c or a,b,-(c)/(2) form a G.P.

If a+b+c=0and|(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 , then show that either x=0 or x=pmsqrt((3)/(2)(a^(2)+b^(2)+c^(2)))

If a^(2),b^(2),c^(2) are in A.P.,then prove that the following are also in A.P.(i) (1)/(b+c),(1)/(c+a),(1)/(a+b) (ii) (a)/(b+c),(b)/(c+a),(c)/(a+b)

If a,b,c are in AP,then prove that (a-c)^(2)=4(b^(2)-ac)

If a!=b!=c, prove that the points (a,a^(2)),(b,b^(2)),(c,c^(2)) can never be collinear.

if a,b,c are in AP, prove that (a-c)^(2) = 4( b^(2) -ac)

If a^(2),b^(2) and c^(2) are in AP then prove that (a)/(b+c),(b)/(c+a) and (c)/(a+b) are also in A.P.

Prove that a(b cos C- os B)=b^(2)-c^(2)