First slide

Binomial theorem for positive integral Index

Question

if $n = (8 + 3 \sqrt{7})^{10}, n \in N$ then the least value of n is

Moderate

A

$(8 + 3 \sqrt{7})^{10} - (8 - 3 \sqrt{7})^{10}$
B

$(8 + 3 \sqrt{7})^{10} + (8 - 3 \sqrt{7})^{10}$
C

$(8 + 3 \sqrt{7})^{10} - (8 - 3 \sqrt{7})^{10} + 1$
D

$(8 + 3 \sqrt{7})^{10} - (8 - 3 \sqrt{7})^{10} - 1$

Solution

Let $f = (8 - 3 \sqrt{7})^{10}$ ,here $0 < f < 1$
$∴ (8 + 3 \sqrt{7})^{10} + (8 - 3 \sqrt{7})^{10}$ is an integer, hence this is the value of n.

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