Q. If $n > \left( 8 + 3\sqrt{7} \right)^{10},\ n \in N,$ then the last value of $n$ is
A) $\left( 8 + 3\sqrt{7} \right)^{10} - \left( 8 - 3\sqrt{7} \right)^{10}$
B) $\left( 8 + 3\sqrt{7} \right)^{10} + \left( 8 - 3\sqrt{7} \right)^{10}$
C) $\left( 8 + 3\sqrt{7} \right)^{10} - \left( 8 - 3\sqrt{7} \right)^{10} + 1$
D) $\left( 8 + 3\sqrt{7} \right)^{10} - \left( 8 - 3\sqrt{7} \right)^{10} - 1$
Explanation
(d)
Let $f = \left( 8 - 3\sqrt{7} \right)^{10}$, here $0 < f < 1$
$\therefore\ \left( 8 + 3\sqrt{7} \right)^{10} + \left( 8 - 3\sqrt{7} \right)^{10}$ is an integer hence, this is the value of $n$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.