Because a is the proportional median of 1-2b and 1+2b. So a 2 = 1-4b 2.

So a 2+4b 2 = 1.

Requirements 1/A 2+ 1/B 2

1/A2+1/B2 = (1/A2+1/B2) (A2+4b2) because A 2+4B 2 = 1.

= 1+4+a^2/b^2+4b^2/a^2

Use the average inequality.

The original formula is greater than or equal to 5+4=9.

So the answer is C.