Solution:
(x+1)6 = x6+6C1 x5.1+ 6C2 x4.12+6C3 x3.13+6C4 x2.14+6C5 x1 .15+6C6.x0.16
⇒x6+6x5+15x4+20x3+15x2+6x+1 -----(1)
(x−1)6=x6+6C1 x5.(−1)+6C2 x4.(−1)2+6C3 x3.(−1)3+6C4 x2.(−1)4+6C5 x1.(−1)5+6C6.x0.(−1)6
⇒x6−6x5+15x4−20x3+15x2−6x+1 -----(2)
Adding (1) and (2)
(x+1)6+(x−1)6 = 2[x6+15x4+15x2+1]
Putting x=2–√x=2
(2–√+1)6+(2–√−1)6 = 2[(2–√)6+15(2–√)4+15(2–√)2+1]
⇒2[8+60+30+1]
⇒2[99]
⇒198
