Question

If a = 9 + 4√5 find
(i) a + 1/ a
(ii) a - 1/a

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Answer 1

$a= 9+4\sqrt{5} \\\frac{1}{a} =\frac{1}{9+4\sqrt{5} } \\\frac{1}{a} =\frac{1(9-4\sqrt{5}) }{(9+4\sqrt{5})(9-4\sqrt{5}) } \\\frac{1}{a} =\frac{9-4\sqrt{5}}{81-80 } \\\\\frac{1}{a} =9-4\sqrt{5}\\\\therefore, \\a+\frac{1}{a} =9+4\sqrt{5} + 9-4\sqrt{5}\\a+\frac{1}{a} =18\\\\also\\a-\frac{1}{a} =9+4\sqrt{5} - 9+4\sqrt{5}\\a-\frac{1}{a} =8\sqrt{5}$