To find: Value of (√2+1)6 + (2 - 1)6
Formula used: (i)
nCr = \(\frac{n!}{(n-r)!(r)!}\)
⇒ 2[(1)a6 + (15)a4 + (15)a2 + (1)]
⇒ 2[a6 + 15a4 + 15a2 + 1] = (a+1)6 + (a-1)6
Putting the value of a =√2 in the above equation
(√2+1)6 + (√2-1)6 = 2[(√2)6 + 15 (√2)4 + 15 (√2)2+ 1]
⇒ 2[8 + 15(4) + 15(2) + 1]
⇒ 2[8 + 60 + 30 + 1]
⇒ 2[99]
⇒ 198
