Question

The sum of (2√2 - 2√3 ) and (√2 - 3√(3 )) is​

Answer 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.