Number of real roots of $3^x+4^x=2^x+5^x$ with proof
66933
Solving an exponential equation with different bases
61148
Finding real roots of $ P(x)=x^8 - x^7 +x^2 -x +15$
90519
Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$
49899
Determine the number of real roots
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
112334
Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
4333
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
22058
Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
29876
Find the number of triples $(x,y,z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$
78190
How to prove that for all natural numbers, $4^n > n^3$?
103803
Prove from first princibles $\frac{x^2-4}{x-4} \rightarrow -5$ as $x \rightarrow 3$
125297
Induction to prove $2n + 3 < 2^n$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
137970
$2 + 2 = 5$ (Fake proof, or ?)