JEE Advance - Mathematics (1988 - No. 16)
Let $$R$$ $$ = {\left( {5\sqrt 5 + 11} \right)^{2n + 1}}$$ and $$f = R - \left[ R \right],$$ where [ ] denotes the greatest integer function. Prove that $$Rf = {4^{2n + 4}}$$
The greatest integer function, denoted by [x], returns the largest integer less than or equal to x.
If $$R = (5\sqrt{5} + 11)^{2n+1}$$, then $$R = (5\sqrt{5} + 11)^{2n+1} + (5\sqrt{5} - 11)^{2n+1}$$.
The expression $$(5\sqrt{5} - 11)$$ is a positive number.
If $$f = R - [R]$$, then $$0 \le f < 1$$.
If $$R = (5\sqrt{5} + 11)^{2n+1}$$, then $$R = (5\sqrt{5} + 11)^{2n+1} - (5\sqrt{5} - 11)^{2n+1}$$.
The expression $$(5\sqrt{5} - 11)$$ is a negative number.
Comments (0)
