`sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6))` का मान क्या है?

Options

A. `2sqrt(2)`
B. `2sqrt(3)`
C. `1+sqrt(5)`
D. `sqrt(5)-1`

Answer

A

Explanation

`(sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6)))`
`implies (sqrt(3)+sqrt(2))-1/((sqrt(3)+sqrt(2)))`
`[(sqrt(5+2sqrt(6))=sqrt((sqrt(3)+sqrt(2))^(2))impliessqrt(3)+sqrt(2)),(a^(2)+b^(2)+2ab=(a+b)^(2))]`
`impliessqrt(3)+sqrt(2)-(1/(sqrt(3)+sqrt(2))xx(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2)))`
`impliessqrt(3)+sqrt(2)-((sqrt(3)-sqrt(2))/(3-2))`
`impliessqrt(3)+sqrt(2)-sqrt(3)+sqrt(2)`
`implies 2sqrt(2)`