`[1/(sqrt(2)+sqrt(3)-sqrt(5))+1/(sqrt(2)-sqrt(3)-sqrt(5))]`
का सरलीकृत मान किसके बराबर है?

Options

A. 1
B. `sqrt(2)`
C. `1/(sqrt(2))`
D. 0

Answer

C

Explanation

`[1/(sqrt(2)+sqrt(3)-sqrt(5))+1/(sqrt(2)-sqrt(3)-sqrt(5))]`
`implies1/((sqrt(2)+sqrt(3))-(sqrt(5)))xx ((sqrt(2)+sqrt(3))+(sqrt(5)))/((sqrt(2)+sqrt(3))+(sqrt(5)))`
`implies sqrt(2)+sqrt(3)+sqrt(5))/(2+3+2sqrt(6)-5)implies(sqrt(2)+sqrt(3)+sqrt(5))/(2sqrt(6))`
Similarly
`implies1/((sqrt(2)-sqrt(3)-(sqrt(5))))+((sqrt(2)-sqrt(3))+(sqrt(5)))/((sqrt(2)-sqrt(3))+sqrt(5))`
`implies (sqrt(2)-sqrt(3)+sqrt(5))/(-2sqrt(6))`
Now put the value in question
`implies((sqrt(2)+sqrt(3)+sqrt(5)))/((2sqrt(6)))-((sqrt(2)-sqrt(3)+sqrt(5)))/'((2sqrt(6)))`
`implies(sqrt(2)+sqrt(3)+sqrt(5)-sqrt(2)+sqrt(3)-sqrt(5))/(2sqrt(6))`
`implies (2sqrt(3))/(2sqrt(6))implies1/(sqrt(2))`