Question

If 1/p=√10+3 then find (p+1/p)2

Answer 1

Answer:

$\frac{1}{p} = \sqrt{10} + 3 \\ p = \frac{1}{ \sqrt{10} + 3} \\ rationalising \: the \: denominator \\ p = \frac{1}{ \sqrt{10} + 3} \times \frac{ \sqrt{10} - 3}{ \sqrt{10} - 3} \\ = \frac{ \sqrt{10} - 3}{ { \sqrt{10} }^{2} - {3}^{2} } \\ = \frac{ \sqrt{10} - 3}{10 - 9} = \sqrt{10} - 3 \\ so \\ p + \frac{1}{p} =( \sqrt{10} - 3) + ( \sqrt{10} + 3) \\ = 2 \sqrt{10}$

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