If `p=2-a`; prove that `a^3+6ap+p^3-8=0`

If p=2-a , then a^(3)+6ap+p^(3)-8 =

Prove that if p=2-a, then a^(3)+6ap+p^(3)-8=0

If p-2^(a), then show that a^(4)+6ap+p^(8)=0

If a,b,c are in A.P.,prove that 8b^(3)-a^(3)-c^(3)=3ac(a+c)

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

If the zeros of the polynomial f(x)=ax^(3)+3bx^(2)+3cx+d are in A.P. prove that 2b^(3)-3abc+a^(2)d=0

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1

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 S_(m)=m^(2) p and S_(n)=n^(2)p , where m ne n in an AP then prove that S_(p) =P^(3)

In /_ABC if 2c cos^(2)((A)/(2))+2a cos^(2)((C)/(2))-3b=0 prove that a b,c are in A.P.