Chapter 4 Methods of Induction and Binomial Theorem Ex 4.2 Solutions

Maharashtra State Board 11th Maths Solutions Chapter 4 Methods of Induction and Binomial Theorem Ex 4.2

(ii) (√5 – √2)⁵
Solution:
Here, a = √5, b = √2 and n = 5.
Using binomial theorem,

(ii)
Solution:
Here, a = 2x, b = and n = 6.
Using binomial theorem,

(ii) (2 + √5)⁵+ (2 – √5)⁵
Solution:


Adding (i) and (ii), we get
∴ (2 + √5 )⁵+ (2 – √5)⁵= (32 + 80√5 + 400 + 200√5 + 250 + 25√5) + (32 – 80√5 + 400 – 200√5+ 250 – 25√5 )
= 64 + 800 + 500
= 1364

(ii) (√5 + 1)⁵– (√5 – 1)⁵= 352
Solution:

(ii) (1.1)⁵
Solution:

(ii) (0.9)⁴
Solution:

(ii) (2x – 1)⁴+ 4(2x – 1)³(3 – 2x) + 6(2x – 1)²(3 – 2x)²+ 4(2x – 1)¹(3 – 2x)³+ (3 – 2x)⁴
Solution: