Question

The mean of p and 1/p is m therefore the mean of P3 and 1/P3 is ?

Answer 1

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$mean \: of \: p \: and \: \frac{1}{p } is \: m \\ = > \: p \: + \frac{1}{p} = 2m \\\large\bold\red{cubing \: both \: sides} \\ {(p + \frac{1}{p} )}^{3} = {(2m)}^{3} \\ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \times p \times \frac{1}{p} (p + \frac{1}{p} ) = {8m}^{3} \\ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \times 2m = 8 {m}^{3} \\ {p}^{3} + \frac{1}{ {p}^{3} } + 6m = {8m}^{3} \\ {p}^{3} + \frac{1}{ {p}^{3} } = {8m}^{3} - 6m \\ \large\bold\red{divide \: by \: 2} \\ \frac{1}{2} ({p}^{3} + \frac{1}{ {p}^{3} } ) = {4m}^{3} - 3m \\ \large\bold\red{ = > } \: mean \: of \: {p}^{3} and \: \frac{1}{ {p}^{3} } \: is \: \small\bold\red{{4m}^{3} - 3m}</p><p>$

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Answer 2

Answer:

this is correct.........................