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Q.
$\sqrt{5}\left[(\sqrt{5}+1)^{50}-(\sqrt{5}-1)^{50}\right]$ is
Binomial Theorem
Solution:
$\sqrt{5}\left[(\sqrt{5}+1)^{50}-(\sqrt{5}-1)^{50}\right]$
$=2 \sqrt{5}\left[{ }^{50} C _{1}(\sqrt{5})^{49}+{ }^{50} C _{3}(\sqrt{5})^{47}+\ldots . .\right]$
$=2\left[{ }^{50} C _{1}(\sqrt{5})^{50}+{ }^{50} C _{3}(\sqrt{5})^{48}+\ldots . .\right]=$ a natural number