A rod of fixed length `k` slides along the coordinates axes, If it meets the axes at `A(a ,0)a n dB(0,b)` , then the minimum value of `(a+1/a)^2+(b+1/b)^2` `0` `8` `k^2=4+4/(k^2)` `k^2+4+4/(k^2)`

Options

A. 0
B. 8
C. `k^2-4+(4)/(k^2)`
D. `k^2+4+(4)/(k^2)`

Answer

D

Explanation

`a^(2) + b^(2) = k^(2)`
`(a + (1)/(a))^(2) + (b + (1)/(b))^(2) = a^(2) + b^(2) + 4 + (1)/(a^(2)) + (1)/(b^(2))`
`= k^(2) + 4 + (k^(2))/(((a^(2) + b^(2))/(2))^(2))`
`= k^(2) + 4 + (4)/(k^(2))`