Question

If f(p)=2-a then prove that a^3+6ap+p^3-8=0

Answer 1

GIVEN
f(p)=2-a

TO PROVE
a^3+6ap+p^3-8=0.....(1)

ANSWER
Let p=2-a sub in (1)
a^3+6a(2-a)+(2-a)^3-8
a^3+12a-6a^2+(2)^3-3(2)^2(a)+3(2)(a)^2-(a)^3-8
a^3+12a-6a^2+8-12a+6a^2-a^3-8
0
Hence,proved.