Решите уравнения: 1)(Х+2)^3=х^3+8 2)(3х-1)^3=27х^3-1

[latex](x+2)^3=x^3+8[/latex] [latex](x^2+4x+4)(x+2)=x^3+8[/latex] [latex]x^3+6x^2+12x+8-x^3-8=0[/latex] [latex]6x^2+12x=0[/latex] [latex]6x(x+2)=0[/latex] [latex] {| {{x+2=0} \atop {6x=0}} \right. {| {{x=-2} \atop {x=0}} \right. [/latex] Ответ: [latex]-2;0[/latex] [latex](3x-1)^3=27x^3-1[/latex] [latex]27 x^{3} -27 x^{2} +9x-1-27x^3+1=0[/latex] [latex]-27x^2+9x=0[/latex] [latex]-9x(3x-1)=0[/latex] [latex]{ |{{-9x=0} \atop {3x-1=0}} {| {{x=0} \atop {3x=1}} \right. {| {{x=0} \atop {x= \frac{1}{3} }} \right. [/latex] Ответ: [latex]0; \frac{1}{3} [/latex]