Question

If 3p+1/3p , then evaluate 3p-1/3p and 81p⁴+1/81p⁴.

Answer 1

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Answer 2

$3p + \frac{1}{3p} = 2\sqrt{3} \\ \\ (3p + \frac{1}{3p})^2 = (2\sqrt{3})^2 \\ \\ = 9p^2 + \frac{1}{9p^2} + 2 = 12 \\ \\ \\ 9p^2 + \frac{1}{9p^2} + 2 - 4 = 12 - 4 \\ \\ = 9p^2 + \frac{1}{9p^2} - 2 = 8 \\ \\ = (3p - \frac{1}{3p})^2 = 8 \\ \\ \bold{3p - \frac{1}{3p} = \sqrt{8} = 2\sqrt{2}} \\ \\ \\ 9p^2 + \frac{1}{9p^2} + 2 = 12 \\ \\ 9p^2 + \frac{1}{9p^2} = 12 - 2 = 10 \\ \\ \\ (9p^2 + \frac{1}{9p^2}) = 10^2 \\ \\ = 81p^4 + \frac{1}{81p^4} + 2 = 100 \\ \\ \\ \bold{81p^4 + \frac{1}{81p^4} = 100 - 2 = 98}$

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