Expand each of the expressions in Exercises 1 to 5: (x/3 + 1/x)⁵

Solution:

By using binomial theorem, the expression (x/3 + 1/x) can be expanded as

(x/3 + 1/x)⁵ = 5C₀ (x/3)⁵ - 5C₁ (x/3)⁴ (1/x) + 5C₂(x/3)³ (1/x)² - 5C₃(x/3)² (1/x)³ + 5C₄(x/3) (1/x)⁴ - 5C₅ (1/x)⁵

Here, we can calculate the binomial coefficients ⁵C₀, ⁵C₁, ... using the nCr formula. Then we get

= 1(x⁵/243) + 5 (x⁴/81) (1/x) + 10 (x³/2) x 7 (1/x²) + 10 (x²/9) (1/x³) + 5 (x/3) (1/x⁴) + 1/x⁵

= x⁵/243 + 5x³/81 + 10x/27 + 10/(9x) + +5/(3x³) + 1/x⁵

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 4

Expand each of the expressions in Exercises 1 to 5: (x/3 + 1/x)⁵

Summary:

We found the expansion of (x/3 + 1/x)⁵ to be x⁵/243 + 5x³/81 + 10x/27 + 10/(9x) + +5/(3x³) + 1/x⁵