Question

(e) If p = 5 + 2√6 and x=1/p, then what will be the value of p^2+ x^2?
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Answer 1

$\large\sf\red{p=5+2√6}$

$\large\sf\red{x=\frac{1}{p}}$

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$\large\sf\green{{p}^{2} = ( {5 + 2 \sqrt{6} )}^{2}}$

$\large\sf\green{25+4√6+24}$

$\large\sf\green{49+4√6}$

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$\large\sf\pink{x=\frac{1}{p}}$

$\longrightarrow$$\large\sf\pink{ \frac{1}{5 + 2 \sqrt{6} }×\frac{5-2√6}{5-2√6}}$

$\longrightarrow$$\large\sf\pink{\frac{ {(5 - 2 \sqrt{6}) }^{2} }{ {(5)}^{2} - {(2 \sqrt{6} )}^{2} }}$

$\longrightarrow$$\large\sf\pink{\frac{ {(5)}^{2} - 2 \times 5 \times 2 \sqrt{6} + {(2 \sqrt{6}) }^{2} }{25 - 24}}$

$\longrightarrow$$\large\sf\pink{\frac{5 - 2 \sqrt{6} }{25 - 24}}$

$\longrightarrow$$\large\sf\pink{5-2√6}$