Question

Si
x-$x^{-1\\}$ = 1
calcular $x^{3} - x^{-3}$

Answer 1

Respuesta:

x³-x⁻³ = 4

Explicación paso a paso:

Si x-x⁻¹ = 1 , Calcular x³-x⁻³

Resolvamos:

(x-x⁻¹)³ = 1³

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

x³-3x²x⁻¹+3xx⁻²-x⁻³ = 1

x³-x⁻³ -3x²x⁻¹+3xx⁻² = 1

x³-x⁻³ -3x+3x⁻¹  = 1

x³-x⁻³ -3(x+x⁻¹)  = 1

x³-x⁻³ -3(1)  = 1

x³-x⁻³ -3 = 1

x³-x⁻³ = 1+3

x³-x⁻³ = 4

Answer 2

Respuesta:

Explicación paso a paso:

x-x^(-1)=1

x^3-3x^2*x(-1)+3x*x^(-2)-x^(-3)=1

x^3-3x+3x^(-1)-x^(-3)=1

x^3-3(x-x^(-1))-x^(-3)=1

x^3-3(1)-x^(-3)=1

x^3-x^(-3)=4