If a, b, c and d are in G.P. show that `(a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2`

If a, b, c, d and p are different real numbers such that (a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd) p + (b^2 + c^2 + d^2) le 0 , then show that a, b, c and d are in GP.

If a, b, c are in A . P , then (a-c)^(2)=

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a, b and c real numbers such that a^(2) + b^(2) + c^(2) = 1, then ab + bc + ca lies in the interval :

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .

If a, b, c, d, e and f are in G.P, then the value of |[a^2,d^2,x],[b^2,e^2,y],[c^2 ,f^2,z]| depends on

If a,b,c are in A.P. and a,mb,c are in G.P. , then a, m^(2)b, are in :

If a,b,c,d and p are distinct non -zero real numbers such that : ( a^(2) + b^(2) +c^(2))p^(2) - 2 ( ab + bc + cd) p + ( b^(2) + c^(2) + d^(2)) le 0 , then a,b,c,d :

If a,b,c are in HP,b,c,d are in GP and c,d,e are in AP, than show that e=(ab^(2))/(2a-b)^(2) .

If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and dx^(2) + 2ex+ f = 0 have a common root if ( d)/( a) , ( e )/( b ) , ( f )/( c ) are in :