Proving $\sqrt{a^2+c^2}+\sqrt{b^2+d^2}\ge \:\sqrt{\left(a+b\right)^2+\left(c+d\right)^2}$
42581
Simple algebra square root inequality
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
156513
Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
134159
Smallest value of $a^2 + b^2 + c^2+ d^2$, given values for $(a+b)(c+d)$, $(a+c)(b+d)$, and $(a+d)(b+c)$
64277
How to prove ${{a}^{a}}{{b}^{b}}\ge {{\left(\frac{a+b}{2}\right)}^{a+b}}$ ?thanks.
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
145352
How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$
111295
Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$