P-5-2 -6-Find p2-1-p2

Given p=5 2√(6) p+1p=5 2√(6)+15 2√(6)=5 2√(6)+5 2√(6)5^2 (2√(6))^2=5 2√(6)+5+2√(6)=10 p^2+1p^2=(p+1p)^2 2=(10)^2 2=100 2=98 ...

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Number Theory: Interesting Results

p=5-2 √6,Find...

Question

$p = 5 - 2 \sqrt{6},$ Find $p^{2} + \frac{1}{p^{2}}$

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Solution

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p = 5 - 2 \sqrt{6},

p^{2} + \frac{1}{p^{2}}

p = 5 + 2 \sqrt{6}

q = \frac{1}{p}

p^{2} + q^{2}

p = 5 + 2 \sqrt{6}, x = \frac{1}{p}

p^{2} + x^{2}

f_{p} (β) = (cos \frac{β}{p^{2}} + i sin \frac{β}{p^{2}}) + (cos \frac{2 β}{p^{2}} + i sin \frac{2 β}{p^{2}}) \dots \dots (cos \frac{β (p - 1)}{p^{2}} + i sin \frac{β (p - 1)}{p^{2}}) + (cos \frac{β}{p} + i sin \frac{β}{p})

lim n \to \infty 1 / f_{n} (π) =

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