How do we prove that $r_1^2+r_2^2+r_3^2+r_4^2=16R^2-a^2-b^2-c^2$
40596
Proving a relation between inradius ,circumradius and exradii in a triangle
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
11868
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
33105
Find the value of $a^2-b^2+c^2$
61022
Diophantine Equations : Solving $a^2+ b^2=2c^2$
106965
How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
44119
Prove that $\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$
100571
Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
110996
Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
145882
How prove this $\frac{a}{(bc-a^2)^2}+\frac{b}{(ca-b^2)^2}+\frac{c}{(ab-c^2)^2}=0$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$