Proving that: $ | a + b | + |a-b| \ge|a| + |b|$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
20346
'Algebraic' way to prove the boolean identity $a + \overline{a}*b = a + b$
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
108704
Help with proof of $|x+y| \geq |x|-|y|$
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
30688
Prove that $\frac{x_1}{1+x_2+x_3+\ldots+x_n}+\frac{x_2}{1+x_1+x_3+\ldots+x_n}+\ldots+\frac{x_n}{1+x_1+x_2+\ldots+x_{n-1}}\ge\frac{n}{2n-1}$.
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
60122
Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
109133
$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$