Value of $ (a+d)(b+c)$
73504
Why $(a+d)(b+c)$ equals $-16$?
31724
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
51321
Prove that $A = B = C = D$
33105
Find the value of $a^2-b^2+c^2$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
87303
Show that $\frac{a}{c} + \frac{b}{d} +\frac{c}{a} + \frac{d}{b}\le-12$
89175
Proof of $(a+b)^{n+1}$
103854
Showing that $Q_n=D_n+D_{n-1}$
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
80095
Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
2019
Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
47737
Find all the possible values of $(a,b,c,d)$.
101476
If $A$, $B$ and $C$ are the angles of a triangle then find the value of $\Delta$
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 $a+b+c+d=2$
30307
Find the value of $k$ in $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \ge \sqrt{a}+\sqrt{b}+\sqrt{c}+k$
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.