Question

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

Answer 1

proved check simple formula use

Answer 2

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