Proving simple Equation has only one root
63505
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
77081
Proving square root of a square is the same as absolute value
158335
Why is this $0 = 1$ proof wrong?
16660
Prove that any positive number has an $n$th root
2408
Show that a polynomial has at least one positive solution/root.
45811
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
112709
$\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
85039
Purely "algebraic" proof of Young's Inequality
41655
Simple equation for $x$ but getting no proof.
32136
How to prove Lucas's Converse of Fermat's Little Theorem without using primitive root?
120457
Show that the equation, $x^3+10x^2-100x+1729=0$ has at least one complex root $z$ such that $|z|>12.$
5410
Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
76347
Shorter proof for some equvalences
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
38662
If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$