Question

Let $R=(5\sqrt{5}+11{)}^{2mn+1},F=R-[R],$ then $RF=$

• A. $1$
• B. $2^n$
• C. $2^{2n}$
• D. $4^{2n+1}$

Answer 1

The correct option is D $4^{2n+1}$

Think of $(5\sqrt{5}+11{)}^{2mn+1}$ as $I+F$ , then $(5\sqrt{5}-11{)}^{2mn+1}$ is only $1-F$ as its integral part is $0$ due to $5\sqrt{5}-11$ being a fraction and hence its power is also a fraction.

Now multiply both to get $RF$ as given in the hint as $(5{\sqrt{5}}^2-{11}^2{)}^{2mn+1}$ is $4^{2n+1}$