The value of $\frac{1}{(9-4\sqrt{5})^2}+\frac{1}{(9+4\sqrt{5})^2}$ is :
Answer & explanation
Correct answer: option 1
$\frac{1}{(9-4\sqrt{5})^2}+\frac{1}{(9+4\sqrt{5})^2}$ =
We know that,
(a + b)2 = (a2 + b2 + 2ab)
(a - b)2 = (a2 + b2 - 2ab)
(a2 - b2) = (a + b) (a - b)
So according to the question,
$\frac{1}{(9-4\sqrt{5})^2}+\frac{1}{(9+4\sqrt{5})^2}$
= [(9 + 4$\sqrt {5}$)2 + (9 - 4$\sqrt {5}$)2]/[(9 - 4$\sqrt {5}$)2 (9 + 4$\sqrt {5}$)2]
= (81 + 80 + 72$\sqrt {5}$ + 81 + 80 - 72$\sqrt {5}$)/(81 - 80)
= 322