Why does $αA^{−1} + (1 −α)B^{−1}\succeq (αA + (1 − α)B)^{−1}$
103367
Is inverse matrix convex?
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
21881
Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
131844
When does $(e^a)^b = e^{ab}$ hold?
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
111295
Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
104922
Inequality $\frac1a + \frac1b + \frac1c \leq \frac{a^8+b^8+c^8}{a^3b^3c^3}$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
48211
When is $(a+b)^n \equiv a^n+b^n$?
141837
Proof of $\sup\{ (n!)^{(\frac{1}{n})}| n ∈ N\} = +∞?$
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$