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NCERT Class XI Mathematics - Binomial Theorem - Solutions

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Question : 31
Total: 36
Evaluate (√3+√2)6−(√3−√2)6
Solution:  
We have (√3+√2)6 =
6
‌
C0(√3)6+
6
‌
C1(√3)5(√2)+
6
‌
C2(√3)4(√2)2+
6
‌
C3(√3)3(√2)3+
6
‌
C4(√3)2(√2)4+
6
‌
C5(√3)(√2)5+
6
‌
C6(√2)6
... (i)
and (√3−√2)6 =
6
‌
C0(√3)6−
6
‌
C1(√3)5(√2)+
6
‌
C2(√3)4(√2)2−
6
‌
C3(√3)3(√2)3+
6
‌
C4(√3)2(√2)4−
6
‌
C5(√3)(√2)5+
6
‌
C6(√2)6
... (ii)
Subtracting (ii) from (i), we get (√3+√2)6−(√3−√2)6
=
2[
6
‌
C1(√3)5(√2)+
6
‌
C3(√2)3(√2)3+
6
‌
C5(√3)(√2)5]

=
2[6(9√3)(√2)+20(3√3)(2√2)+6(√3)(4√2)]

= 2 [54√6+120√6+24√6] = 2 (198√6) = 396 √6
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