Câu cuối hay nha
Đặt
[tex]a+b=x \\ab=y\\\rightarrow a^2+b^2=x^2-2y[/tex]
Thay vô trên có:
[tex]x^2-2y+\frac{(y+1)^2}{x^2}\geq 2\\\rightarrow x^2(x^2-2y)+(y+1)^2-2x^2\geq 0\\\rightarrow x^4-2x^2y+y^2+2y+1-2x^2\geq 0\\\rightarrow x^4+y^2+1-2x^2y+2y-2x^2\geq 0\\\rightarrow (x^2-y-1)^2\geq 0 (ok!!)[/tex]