Expand each of the expressions in Exercises 1 to 5: (x + 1/x)⁶

Solution:

By using binomial theorem, the expression (x + 1/x)⁶ can be expanded as

(x + 1/x)⁶ = ⁶C₀ (x)⁶ + ⁶C₁ (x)⁵ (3) + ⁶C₂ (x)⁴ (1/x)² + ⁶C₃ (x)³ (1/x)³ + ⁶C₄ (x)² (1/x)⁴ - ⁶C₅ (x)(1/x)⁵ + ⁶C₆(1/x)⁶

Here, we can calculate the binomial coefficients ⁶C₀, ⁶C₁, ... using the nCr formula. Then we get

= 1(x⁶) + 6x⁵ (1/x) + 15x⁴ (1/x²) + 20x³ (1/x³)

= 15x² (1/x⁴) + 6(x) (1/x⁵) + (1/x⁶)

= x⁶ + 6x⁴ + 15x² + 20 + 15/x² + 6x⁴ + 1/x⁶

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 5

Expand each of the expressions in Exercises 1 to 5: (x + 1/x)⁶

Summary:

We found the expansion of (x + 1/x)⁶ to be x⁶ + 6x⁴ + 15x² + 20 + 15/x² + 6x⁴ + 1/x⁶