Given that $a > 0$, $b > 0$ and $b > a$, prove the solution of $a^b = b^a$
18761
Given that $x^y=y^x$, what could $x$ and $y$ be?
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
20626
Prove that $x^y < y^x$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
15730
Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
77212
Show that for any real constants a and b, where b > 0, (n + a) b = Θ(n b ).
38849
Solve $x^y \, = \, y^x$
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
47949
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$