`[(sqrt(3)+1)/(sqrt(3)-1)+(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(3)-1)/(sqrt(3)+1)+(sqrt(2)-1)/(sqrt(2)+1)]`
का सरलीकरण मान है।

Options

A. 10
B. 12
C. 14
D. 18

Answer

A

Explanation

`((sqrt(3)+1)/(sqrt(3)-1)+(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(3)-1)/(sqrt(3+1))+(sqrt(2)-1)/(sqrt(2)+1))`
`((sqrt(3)+1))/((sqrt(3)-1))xx((sqrt(3)+1))/((sqrt(3)+1))+(sqrt(2)+1)/(sqrt(2)-1)xx(sqrt(2)+1)/(sqrt(2)+1)`
`+(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1)+(sqrt(2)-1)/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`implies((sqrt(3)+1)^(2))/(3-1)+((sqrt(2)+1)^(2))/(2-1)+((sqrt(3)-1)^(2))/(3-1)`
`+((sqrt(2)-1)^(2))/(2-1)`
`implies(3+1+2sqrt(3))/2+(2+1+2sqrt(2))/1+(3+1-2sqrt(3))/2`
`+(2+1-2sqrt(2))/1`
`2+sqrt(3)+3+2sqrt(2)+2-sqrt(3)+3-2sqrt(2)`
`=10`