11.
[tex]x^4+(x-3)^2=x^4-2x^2+1+3x^2-6x+3+5=(x^2-1)^2+3(x-1)^2+5\geq 5[/tex]
Đẳng thức xảy ra khi $x=1$
12.
[tex]f(x+\frac{1}{x})=x^3+\frac{1}{x^3}=(x+\frac{1}{x})(x^2+\frac{1}{x^2}-1)=(x+\frac{1}{x})((x+\frac{1}{x})^2-3)\\\Rightarrow f(x)=x(x^2-3)=x^3-3x[/tex]