Question

Ayuda por favor con este ejercicio de algebra

Answer 1

Respuesta:

n = 18(√2 - 1)

Explicación paso a paso:

(√2x¹⁷ + x⁻¹)ⁿ   = (y + z)ⁿ  

y = √2x¹⁷

z = x⁻¹

Utilizar:  

tₐ = Cⁿₐ yⁿ⁻ᵃ zᵃ  

a = n - 1

tₙ₋₁ = Cⁿₙ₋₁ yⁿ⁻⁽ⁿ⁻¹⁾ zⁿ⁻¹  

tₙ₋₁ = [n! / ((n - 1)!(n - (n - 1))!)] yⁿ⁻⁽ⁿ⁻¹⁾ zⁿ⁻¹  

tₙ₋₁ = [n (n - 1)! / ((n - 1)!(n - n + 1)!)] yⁿ⁻ⁿ⁺¹ zⁿ⁻¹  

tₙ₋₁ = [n / (1)!] y zⁿ⁻¹  

tₙ₋₁ = n y zⁿ⁻¹  

tₙ₋₁ = n √2x¹⁷ (x⁻¹)ⁿ⁻¹  

tₙ₋₁ = n √2x¹⁷ x⁻ⁿ⁺¹

tₙ₋₁ = n√2x¹⁸⁻ⁿ

18 - n = n√2

18 = n + n√2

18 = n(1 + √2)

18 / (1 + √2) = n

n = 18 / (1 + √2)

n = 18 / (√2 + 1)

n = 18(√2 - 1) / (√2 + 1)(√2 - 1)

n = 18(√2 - 1) / (√2² - 1²)

n = 18(√2 - 1) / (2 - 1)

n = 18(√2 - 1)