Question

(3X -2/X )² + 6 (3X -2/X ) + 5 = 0 , alguien que sepa resolver esto es sbre inecuaciones

Answer 1

Respuesta:

x₁ = -1

x₂ = -2

x₃ = 1/3

x₄ = 2/3

Explicación paso a paso:

$(3x-\frac{2}{x} )^{2} +6(3x-\frac{2}{x} )+5=0$

$(9x^{2} -2*(3x)*(\frac{2}{x} )+\frac{4}{x^{2} } )+18x-\frac{12}{x} +5=0$

$9x^{2} -12+\frac{4}{x^{2} } +18x-\frac{12}{x} +5=0$

$x^{2} (9x^{2} -12+\frac{4}{x^{2} } +18x-\frac{12}{x} +5)=0$

$x^{2} (9x^{2} +\frac{4}{x^{2} } +18x-\frac{12}{x} -7)=0$

$9x^{4} +4+18x^{3} -12x-7x^{2} =0$

$9x^{4} +18x^{3} -7x^{2} -12x+4=0$

Utilizando el metodo de Ruffini , obtenemos;

$9x^{4} +18x^{3} -7x^{2} -12x+4=(x + 1)(x + 2)(x - 1/3)(x - 2/3)$

Resolviendo;

$(x + 1)(x + 2)(x - 1/3)(x - 2/3) = 0$

x₁ = -1

x₂ = -2

x₃ = 1/3

x₄ = 2/3