Question

Prove that (√5+1)^5 - (√5-1)^5 =352​

Answer 1

Answer:

352

Step-by-step explanation:

Hi,

Expanding (√5 + 1)⁵ using binomial expansion we get

(√5 + 1)⁵ = ⁵C₀(√5)⁵ + ⁵C₁(√5)⁴ + ⁵C₂(√5)³ + ⁵C₃(√5)² + ⁵C₄(√5)

+ ⁵C₅-------------(1)

(√5 - 1)⁵ = ⁵C₀(√5)⁵ - ⁵C₁(√5)⁴ + ⁵C₂(√5)³ - ⁵C₃(√5)² + ⁵C₄(√5)

- ⁵C₅-------------(2)

Subtracting (1) - (2), we get

(√5 + 1)⁵ - (√5 - 1)⁵

= 2[⁵C₁(√5)⁴ + ⁵C₃(√5)² + ⁵C₅]

= 2[5*25 + 10*5 + 1]

= 2[125 + 50 + 1]

= 2[176]

= 352

Hope, it helps !

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