$X>0$, $Y>0$ and $X^2+Y ^3\geq X^3+Y^4$. Prove that $X^3+Y ^3\leq 2$
36507
If $x,y>0$ and $x^2+y^3\ge x^3+y^4$, prove that $x^3+y^3 \le 2$.
77026
Proof with inequalities
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
20626
Prove that $x^y < y^x$
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
83386
Inequality with exponents $x^x+y^y \ge x^y +y^x$
90896
proof of inequality $e^x\le x+e^{x^2}$
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
8207
Can I prove this inequality algebraically?
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$