Prove that $\sqrt{a}+ \sqrt{b} + \sqrt{c} + \sqrt{d} \le 10 $
135550
Inequality question­
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
23694
Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
97057
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
17100
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
147648
Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$