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

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

Text Solution

Verified by Experts

We have
`p=2-a`
`rArr a+p-2=0`
`rArr x+y+z=0, " where " a=x,y and (-2)=z`
` rArr x^3+y^3+z^3=3xyz " "[because x+y+z=0 rArr x^3+y^3+z^3=3xyz]`
`rArr a^3+p^3+(-2)^3=3xx a xx pxx (-2)`
`rArr a^23+6ap+p^3-8=0`
Hence, `a^3+6ap+p^3-8=0`.
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