`12/(3+sqrt(5)+2sqrt(2))` के बराबर है।

Options

A. `1-sqrt(5)+sqrt(2)+sqrt(16)`
B. `1+sqrt(5)+sqrt(2)-sqrt(10)`
C. `1+sqrt(5)+sqrt(2)+sqrt(10)`
D. `1-sqrt(5)-sqrt(2)+sqrt(10)`

Answer

B

Explanation

`12/(3+sqrt(5)+2sqrt(2))`
`=(12(3+sqrt(5)-2sqrt(2)))/([(3+sqrt(5))+2sqrt(2)][(3+sqrt(5))-2sqrt(2)])`
`implies(12(3+sqrt(5)-2sqrt(2)))/((3+sqrt(5))^(2)-(2sqrt(2))^(2))`
`= (12(3+sqrt(5)-2sqrt(2)))/(9+5+6sqrt(5)-8)`
`implies(12(3+sqrt(5)-2sqrt(2)))/(6sqrt(5)+6)=(2(3+sqrt(5)-2sqrt(2)))/(sqrt(5)+1)`
`implies(2(3+sqrt(5-2)sqrt(2))(sqrt(5)-1))/((sqrt(5)-1)(sqrt(5)+1))`
`implies (2(3sqrt(5)+5-2sqrt(10)-3-sqrt(5)+2sqrt(2)))/(5-1)`
`implies2(2sqrt(5)+2sqrt(2)-2sqrt(10)+2)/4`
`implies2xx2(sqrt(5)+sqrt(2)-sqrt(10)+1)/4`
`impliessqrt(5)+sqrt(2)-sqrt(10)+1`