The value of ( 2 + 1)^6 + ( 2 - 1)^6 will be - Vidyadip

Question

The value of ${(\sqrt 2 + 1)^6} + {(\sqrt 2 - 1)^6}$ will be

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Answer

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, $n = 6,x = \sqrt 2 ,a = 1$; $^6{C_2} = 15,{\,^6}{C_4} = 15,{\,^6}{C_6} = 1$

$\therefore \,\,{(\sqrt 2 + 1)^6}{(\sqrt 2 - 1)^6} = 2[{(\sqrt 2 )^6} + 15.{(\sqrt 2 )^4}.1$
$ + 15{(\sqrt 2 )^2}.1 + 1.1]$

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

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