" 3."p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2)

Factorise p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2) .

Show that (a^(2) +ab+b^(2)) ,(c^(2) +ac +a^(2)) and ( b^(2) +bc+ c^(2)) are in AP, if a,b,c are in AP.

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible

If a,b,c are in A.P.,prove that: (a-c)^(2)=4(a-b)(b-c)a^(2)+c^(2)+4ac=2(ab+bc+ca)a^(3)+c^(3)+6abc=8b^(3)

If a^(2) + 2bc, b^(2) + 2ac, c^(2) + 2ab are in A.P then prove that (1)/(b-c), (1)/(c-a) and (1)/(a-b) are in A.P.

In a DeltaABC the angles A, B, C are in A.P. show that 2cos""(A-C)/2=(a+c)/sqrt((a^(2)-ac+c^(2)))

If acos^(2).(C)/(2)+c"cos"^(2)(A)/(2)=(3b)/(2), then show that a, b , c are in A.P