How do I prove $2xy ≤ x^2+y^2$?
27911
How can I prove that $xy\leq x^2+y^2$?
156881
How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
31544
How to prove that this polynomial is larger than another for positive reals?
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
77026
Proof with inequalities
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
31937
How do I prove equality of x and y?
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
126445
Proving the second root of a quadratic equation
14677
Proving the exponential inequality: $x^y+y^x\gt1$
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
126032
Proving a certain inequality
83386
Inequality with exponents $x^x+y^y \ge x^y +y^x$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$