Question

if p=2-a , prove that a^3 + 6ap + p^3-8=0 ​

Answer 1

Answer

Given ,

• p = 2-a

To Prove ,

• a^3 + 6ap + p^3-8=0

We have ,

• p = 2-a => a+p-2=0

Now ,

=> a^3 +6ap + p^3 - 8 = a^3 + p^3 +(-2)^3-3ap(-2)

=> { a+p+(-2)}{a^2+p^2+(-2)-ap-p(-2)-a(-2)}

=> ( a+p-2)(a^2 + p^2 +4-ap+2p+2a )

=> 0 × (a^2 + p^2 +4-ap+2p+2a )

=> 0

Hence , Proved !