$3) a^3+b^3\leq a^4+b^4$$\Leftrightarrow 2(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow (a+b)(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow a^4+b^4-a^3b-ab^3\geq 0$$\Leftrightarrow (a^3-b^3)(a-b)\geq 0$$\Leftrightarrow (a-b)^2(a^2+ab+b^2)\geq 0$ (luôn đúng)
$3) a^3+b^3\leq a^4+b^4$$\Leftrightarrow 2(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow (a+b)(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow a^4+b^4-a^3b-ab^3\geq 0$$\Leftrightarrow (a^3-b^3)(a+b)\geq 0$$\Leftrightarrow (a-b)^2(a^2-ab+b^2)\geq 0$ (luôn đúng)
$3) a^3+b^3\leq a^4+b^4$$\Leftrightarrow 2(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow (a+b)(a^3+b^3)\leq 2(a^4+b^4)$$\Leftrightarrow a^4+b^4-a^3b-ab^3\geq 0$$\Leftrightarrow (a^3-b^3)(a
-b)\geq 0$$\Leftrightarrow (a-b)^2(a^2
+ab+b^2)\geq 0$ (luôn đúng)