Question

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Answer 1

Respuesta:

A) 52

Explicación paso a paso:

x  +  x⁻¹ = 4

x  +  1/x = 4

----

(x  +  1/x)³ = (4)³

x³ + 3(x)²(1/x) + 3(x)(1/x)² + (1/x)³ = 64

x³+ (1³/x³) + 3x + (3/x) = 64

x³ + 1/x³ + 3 ( x + 1/x) = 64

x³ + x⁻³ + 3 ( 4) = 64

x³ + x⁻³  = 64 - 12

x³ + x⁻³ = 52

Answer 2

Respuesta:

Es la A

Explicación paso a paso:

Si: x + x⁻¹ =4. Halla el valor de: E = x³ + x⁻³

Resolvamos:

(x + x⁻¹) = (4)³

(x)³ + 3(x)²(x⁻¹) + 3(x)(x⁻¹)² + (x⁻¹)³ = 64

x³ + 3(x²)(x⁻¹) + 3(x)(x⁻²) + x⁻³ = 64

x³ + 3x + 3x⁻¹ + x⁻³ = 64

x³ + 3(x + x⁻¹) + x⁻³ = 64

x³ + 3(4) + x⁻³ = 64

x³ + x⁻³ +12 = 64

x³ + x⁻³ = 64-12

x³ + x⁻³ = 52

Hallamos E:

E = x³ + x⁻³

E = 52

Por lo tanto, el valor de E es 52