Binomial Theorem And Its Simple Applications Question 1
Question: The value of $ {{(\sqrt{2}+1)}^{6}}+{{(\sqrt{2}-1)}^{6}} $ will be
[RPET 1997]
Options:
A) - 198
B) 198
C) 99
D) - 99
Show Answer
Answer:
Correct Answer: B
Solution:
- $ {{(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 $
BETA
