Question

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Answer 1

Respuesta:

Es la e

Explicación paso a paso:

Si: a + b = 3 y ab=1; Halla : a⁶ + b⁶

Datos:  

a + b = 3

ab = 1

Resolvamos:  

(a + b)² = a² + 2ab + b²  

(a + b)² = a² + b² + 2ab  

(3)² = a² + b² + 2(1)  

9 = a² + b²+2  

9-2 = a² + b²  

7  = a² + b²

(a² + b²)² = a⁴ + 2ab + b⁴  

(a² + b²)² = a⁴ + b⁴ + 2ab  

(7)² = a⁴ + b⁴ + 2(1)  

49 = a⁴ + b⁴ +2  

49-2 = a⁴ + b⁴  

47  = a⁴ + b⁴

a⁶ + b⁶ = (a² + b²)(a⁴ -a²b² + b⁴)

a⁶ + b⁶ = (a² + b²)(a⁴ -(ab)² + b⁴)

a⁶ + b⁶ = (a² + b²)(a⁴ + b⁴-(ab)²)

a⁶ + b⁶ = (7)(47-(1)²)

a⁶ + b⁶ = (7)(47-1)

a⁶ + b⁶ = (7)(46)

a⁶ + b⁶ = 322

Por lo tanto, el valor de  a⁶ + b⁶ es 322