Question

Let $(5+2\sqrt{6}{)}^n=p+f$, where $n\epsilon N$ and $p\epsilon N$ and $0<f<1$, then the value of $f^2-f+pf-p$ is

• A. a natural number
• B. a negative integer
• C. a prime number
• D. an irrational number

Answer 1

The correct option is B a negative integer

$f^2-f+pf-p$

$=f(f+p)-(f+p)$

$=(f-1)(f+p)$

which is negative; $\because f<1$