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