The harmonic mean of the roots of the equation `:`
`( 5+ sqrt( 2))x^(2) - ( 4+sqrt( 5))x + 8 + 2 sqrt( 5) = 0` is `:`

Answer

4

Explanation

We have `(5+sqrt(2))x^(2)-(4+sqrt(5))x+8+2sqrt(5)=0`
`:.` Sum of the roots `=(4+sqrt(5))/(5+sqrt(2))`
and product of the roots `=(8+2sqrt(5))/(5+sqrt(2))`
and product of the roots `=(8+2sqrt(5))/(5+sqrt(2))`
`:.` The harmonic mean of the roots
`=(2xx"Product of the roots")/("Sum of the roots")=(2xx(8+2sqrt(5)))/((4+sqrt(5)))=4`