Math, asked by Adarsh2421, 1 year ago

If p = 2- a, then prove that a 3 + 6 a p + p 3 – 8 = 0 prove

Answers

Answered by Umeshlohani
5

proved check simple formula use

Attachments:
Answered by pandaXop
5

Step-by-step explanation:

Given:

  • p = 2 – a

To Prove:

  • a³ + 6ap + p³ – 8 = 0

Proof:- We have p = 2 – a

\implies \: a + p - 2 = 0 \\  \\\implies \: x + y + z = 0, where \: a = x , p = y  \: and( - 2) = z \\  \\ \implies \: {x}^{3}  +  {y}^{3}  +  {z}^{3}  = 3xyz \: [ \: since \: x + y + z = 0 =  >  {x}^{3}  +  {y}^{3}  +  {z}^{3}  = 3xyz \\  \\ \: \implies {a}^{3}  +  {p}^{3}  + ( { - 2}^{3} ) = 3 \times a \times p \times ( - 2) \\  \\ \implies \:  {a}^{3}  + 6ap +  {p}^{3}  - 8 = 0

Hence, Proved

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