3)a3+b3≤a4+b4⇔2(a3+b3)≤2(a4+b4)⇔(a+b)(a3+b3)≤2(a4+b4)⇔a4+b4−a3b−ab3≥0$\Leftrightarrow (a^3-b^3)(a+b)\geq 0$$\Leftrightarrow (a-b)^2(a^2-ab+b^2)\geq 0$ (luôn đúng)
3)a3+b3≤a4+b4⇔2(a3+b3)≤2(a4+b4)⇔(a+b)(a3+b3)≤2(a4+b4)⇔a4+b4−a3b−ab3≥0$\Leftrightarrow (a^3-b^3)(a
-b)\geq 0$$\Leftrightarrow (a-b)^2(a^2
+ab+b^2)\geq 0$ (luôn đúng)