Question

pls dont answer if u dont know

Answer 1

63773/62737

=63748√5

so,

439636+7252

=826636371

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Answer 2

$\huge{\underline{\bf{\red{Solution:-}}}}$

$\mapsto \rm\: \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} }=a+5\sqrt{b} \: \\ \\ \small\rm\: \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } = a + 5 \sqrt{b} \\ \\ \small \rm\: \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5} ) }{ {3}^{2} - { \sqrt{5} }^{2} } - \frac{(7 - 3 \sqrt{5} )(3 + \sqrt{5} )}{ {3}^{2} - { \sqrt{5} }^{2} } \\ \\\small \rm\: \frac{21 - 7 \sqrt{5} + 9 \sqrt{5} - 15 - 21 - 7 \sqrt{5} + 15 }{4} = a + 5 \sqrt{b} \\ \\ \mapsto \rm\: \frac{ - 14 \sqrt{5} + 18 \sqrt{5} }{4} = a + 5 \sqrt{b} \\ \\\mapsto \rm\: \frac{4 \sqrt{5} }{4} = a + 5 \sqrt{b} \\ \\\mapsto \rm\: \sqrt{5} = a + 5 \sqrt{b} \: \: \: \: \: .........(i) \\ \\ \mapsto \bf\:a = - 5 \sqrt{b} + \sqrt{5}$

From equation (i)

$\mapsto \rm\: \sqrt{5} = a + 5 \sqrt{b} \: \\ \\\mapsto \rm\:a + 5\sqrt{b} = \sqrt{5} \\ \\ \mapsto \rm\:5 \sqrt{b} = \sqrt{5} - a \\ \\ \mapsto \rm\: \sqrt{b} = \frac{ \sqrt{5} - a}{5} \\ \\ \mapsto \bf\:b = ( \frac{ \sqrt{5} - a}{5}) ^{2}$

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