Maharashtra State BoardHSC Science (General) 11th
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Expand: (3+2)4 - Mathematics and Statistics

Sum

Expand: `(sqrt(3) + sqrt(2))^4`

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Solution

Here a = `sqrt(3)`, b = `sqrt(2)` and n = 4.

Using binomial theorem,

`(sqrt(3) + sqrt(2))^4`

`= ""^4"C"_0 (sqrt(3))^4 (sqrt(2))^0 + ""^4"C"_1 (sqrt(3))^3 (sqrt(2))^1 + ""^4"C"_2 (sqrt(3))^2 (sqrt(2))^2 + ""^4"C"_3 (sqrt(3))^1 (sqrt(2))^3 + ""^4"C"_4 (sqrt(3))^0 (sqrt(2))^4` 

Since 4C0 = 4C4 = 1, 4C1 = 4C3 = 4,

4C2 = `(4 xx 3)/(2 xx 1)` = 6

 ∴ `(sqrt(3) + sqrt(2))^4`

`= 1(9) (1) + 4(3sqrt(3)) (sqrt(2)) + 6(3)(2) + 4(sqrt(3)) (2sqrt(2)) + 1(1)(4)`

= `9 + 12sqrt(6) + 36 + 8sqrt(6) + 4`

= `49 + 20sqrt(6)`

Concept: Binomial Theorem for Positive Integral Index
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.2 | Q 1. (i) | Page 77
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