If `a+b+c=0, an^(2)+bn+c=0` and `a+bn+cn^(2)=0` where `n!=0, 1`, then prove that `a=b=c=0`

If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b^2> or = or < ac .

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 prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

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 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 aN = {ax|x in N} and bN nn cN = dN , where b,c epsilon N , then

If aN = {ax|x in N} and bN nn cN = dN , where b,c epsilon N , then

If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432) .

If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in GP.

If aN = {an : n in N} and bn nn cN = dN where a, b, c, d in N and b, c are relatively prime then