Let us solve the given expression:
(x + 1) 6 + (x – 1) 6
Now, the above expression can be expressed as,
(x + 1) 6 + (x – 1) 6 = 2 [6C0 x6 + 6C2 x4 + 6C4 x2 + 6C6 x0]
= 2 [x6 + 15x4 + 15x2 + 1]
Now,
Lets evaluate the expression:
(√2 + 1)6 + (√2 – 1)6
Therefore consider, x = √2 then we get,
(√2 + 1)6 + (√2 – 1)6 = 2 [x6 + 15x4 + 15x2 + 1]
= 2 [(√2)6 + 15 (√2)4 + 15 (√2)2 + 1]
= 2 [8 + 15 (4) + 15 (2) + 1]
= 2 [8 + 60 + 30 + 1]
= 198
