Question

please solve the above question​

Answer 1

[tex]\mathfrak{\huge{Answer:-}} \\ i) \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \\ = \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ = \frac{(7 + 3 \sqrt{5} )(7 + 3 \sqrt{5}) }{(7 -3 \sqrt{5} )(7 + 3 \sqrt{5})} \\ = \frac{ {(7 + 3 \sqrt{5}) }^{2} }{ {(7)}^{2} - {(3 \sqrt{5}) }^{2} } \\ = \frac{49 + 45 + 42 \sqrt{5} }{49 - 45} \\ = \frac{94 + 42 \sqrt{5} }{4} \\ = \frac{2(47 + 21 \sqrt{5}) }{4} \\ = \frac{47 + 21 \sqrt{5} }{2} \\ [/tex]