Question

Prove that if a =9-4√5 find the value of a+ 1/a

Answer 1

Answer:

Step-by-step explanation:

a= 9-4√5

=>1/a= 9+4√5(Rationalising 1/9-4√5)

=>a+1/a= 9-4√5+9+4√5

=>a+1/a= 18(Ans)

Answer 2

GIVEN :-

$a = 9 - 4 \sqrt{5} \\ \\ \implies \frac{1}{a} = \frac{1}{9 - 4 \sqrt{5} } \\ \\ = \frac{1(9 + 4 \sqrt{5}) }{9 - 4 \sqrt{5}(9 + 4 \sqrt{5}) } \\ \\ = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ = 9 + 4 \sqrt{5} \\ \\ \\ now \\ a + \frac{1}{a} = 9 - 4 \sqrt{5} + 9 + 4 \sqrt{5} \\ \\ \\ = 18(ans)$