The sum of (2√2 - 2√3 ) and (√2 - 3√(3 )) is
Answers
Answered by
1
Answer:
S=(2
1/2
+3
1/3
+5
1/5
)
10
By multinomial expansion,
⇒S=∑
(r
1
)!(r
2
)!(r
3
)!
(10)!
(2
1/2
)
r
1
(3
1/3
)
r
2
(5
1/5
)
r
3
⇒r
1
+r
2
+r
3
=10
∴r
1
=2λ
1
r
2
=3λ
2
⇛ For any term to be rational.
r
3
=5λ
3
Case 1→λ
1
=λ
2
=0;λ
3
=2
Case 2→λ
2
=λ
3
=0;λ
1
=5
Case 3→λ
1
=λ
2
=λ
3
=1
Case 4→λ
1
=λ
2
=2;λ
3
=0
∴ Sum of coefficient =
4!6!
10!
×2
2
.3
2
+
10!
10!
×5
2
+
10!
10!
×2
5
+
2!3!5!
10!
×2×3×5
=83217.
Similar questions