The value of (√2+1)6 + (√2−1)6 will be

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Question

The value of

{(\sqrt{2} + 1)}^{6}

+

{(\sqrt{2} - 1)}^{6}

will be

Options:

A . -198

B . 198

C . 99

D . -99

Answer: Option B
:
B

(x + a)^{n}

+

(x - a)^{n}

= 2

[x^{n} +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{4} x^{n - 4} a^{4} +^{n} C_{6} x^{n - 6} a^{6} + . . . . . . .]

Here, n = 6, x =

\sqrt{2}

, a = 1;

^{6} C_{2}

= 15,

^{6} C_{4}

= 15,

^{6} C_{6}

= 1
∴ (

\sqrt{2} + 1)^{6}

+ (

\sqrt{2} - 1)^{6}

= 2

[(\sqrt{2})^{6} + 15. (\sqrt{2})^{4} .1 + 15 (\sqrt{2})^{2} .1 + 1.1]

= 2 [8 + 15 \times 4 + 15 \times 2 + 1] = 198

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