Question

Evaluate : (√3+√2)⁶-(√3-√2)⁶

Answer 1

To find : Value of (√3+√2)⁶-(√3-√2)⁶

Formula used: (i)

ⁿC_r = \(\frac{n!}{(n-r)!(r)!}\)

(ii) (a+b)n = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + … +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ 

= 2[(6)a⁵b + (20)a³b³ + (6)ab⁵] 

⇒ (a+b)⁶ - (a-b)⁶ = 2[(6)a⁵b + (20)a³b³ + (6)ab⁵] 

Putting the value of a = √3 and b = √2 in the above equation

(√3 + √2)⁶ - (√3 - √2)⁶

⇒ 2[(6)(√3)⁵(√2)+(20)(√3)³(√2)³ + (6)(√3)(√2)⁵]

⇒ 2[54(√6) + 120(√6) + 24 (√6)]

⇒ 396√6