First slide

Binomial theorem for positive integral Index

Question

The value of $\{(\sqrt{2} + 1)^{5} + (\sqrt{2} - 1)^{5}\}$ , is

Moderate

A

58
B

$58 \sqrt{2}$
C

42
D

$42 \sqrt{2}$

Solution

Using binomial expansion, we have
$\begin{array}{l} (\sqrt{2} + 1)^{5} + (\sqrt{2} - 1)^{5} = 2 \{(\sqrt{2})^{5} + 10 (\sqrt{2})^{3} + 5 \sqrt{2}\} \\ (\sqrt{2} + 1)^{5} + (\sqrt{2} - 1)^{5} = 2 {4 \sqrt{2} + 20 \sqrt{2} + 5 \sqrt{2}} = 58 \sqrt{2} \end{array}$

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