If R = `(sqrt(2) + 1)^(2n+1) and f = R - [R]`, where [ ]
denote the greatest integer function, then [R] equal

Options

A. f + `(1)/("f")`
B. f - `(1)/("f")`
C. `(1)/("f")`-f
D. None

Answer

C

Explanation

Let G = `(sqrt(2)-1)^(2n+1)" "...(i)` ltBrgt `OltGlt1` ltBrgt R-G= `(sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)`
f+[R] -G= An even Integer
f-G=0`rArr`f=G (`0ltflt1`)
`(1)/("f")=(1)/(G)=(1)/((sqrt(2)-1)^(2n+1))=R` ltBrgt `(1)/("f")=RrArr" "(1)/("f")=[R]+"f"`
`[R]=(1)/"(f)"`-f