User cosmo5

15 votes

Easy way to see that $(x^2 + 5x + 4)(x^2 + 5x + 6) - 48 = (x^2 + 5x + 12)(x^2 + 5x - 2)$?

answered Nov 22, 2020 at 17:00

11 votes

Accepted

Where did I go wrong in applying the factor theorem?

answered Oct 19, 2020 at 12:10

11 votes

Partition the remaining rectangle into equal parts.

answered Jan 16, 2021 at 12:30

10 votes

Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.

answered Dec 1, 2020 at 15:56

8 votes

Can $S_n=a_1a_2+a_2a_3+\cdots+a_na_1=0$ if $a_i=±1$ for $n=28$ and $n=30$?

answered Jan 10, 2021 at 13:30

8 votes

(AIME 1994) $ \lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \ldots + \lfloor \log_2 n \rfloor = 1994 $

answered Oct 28, 2020 at 11:39

7 votes

Accepted

SMO problem: Sequence and series.

answered Mar 7, 2021 at 13:11

6 votes

Accepted

Finding angle in a triangle with one median and an isosceles triangle in it

answered Mar 14, 2021 at 17:18

6 votes

Prove that the lines parallel to the angle bisectors through the midpoints of sides of a triangle are concurrent at the Spieker center

answered Apr 17, 2021 at 5:29

6 votes

Accepted

A problem related to $\int_{0}^{1} f(x)(x-f(x))dx=1/12$

answered Nov 11, 2020 at 8:57

6 votes

Suppose $x$ and $y$ are unequal real numbers

answered Nov 11, 2020 at 11:16

6 votes

Visual proof for $[\triangle ABC] = rs$?

answered Nov 11, 2020 at 17:37

6 votes

summing this binomial series

answered Sep 21, 2020 at 16:27

6 votes

Accepted

Probability of lines in a pentagon intersecting internally or at vertices.

answered Feb 11, 2021 at 18:08

6 votes

Exponent equation with common power

answered Feb 12, 2021 at 21:14

5 votes

Finding solutions to $[x]^2 + 2[x]-3x=0$

answered Feb 11, 2021 at 18:25

5 votes

Accepted

Solve integral $\int\frac{1}{(x^2-1)\sqrt{x^2+1}}dx$

answered Jan 24, 2021 at 19:48

5 votes

Accepted

For which $n$, $n=x+y+xy$ has no solution in natural numbers?

answered Jan 7, 2021 at 14:11

5 votes

Accepted

How many rectangles can be found in this shape?

answered Dec 31, 2020 at 14:50

5 votes

Accepted

Let $P$ be a $30$-sided polygon inscribed in a circle. Find the value of $\frac{N}{100}$.

answered Dec 5, 2020 at 13:20

5 votes

Accepted

Four-letter words from the word MEDITERRANEAN such that the first letter is R and the fourth letter is E

answered Nov 22, 2020 at 16:02

5 votes

Solve the inequality $x^4-3x^2+5\ge0$

answered Oct 21, 2020 at 15:26

5 votes

Accepted

Number of Dispersion Lines in A Square Dot Matrix

answered Oct 30, 2020 at 8:29

4 votes

How to solve $x^2 \equiv 12 \pmod {13}$?

answered Nov 6, 2020 at 18:44

4 votes

Accepted

Factorizing $12x^3 - 8x^2 - 3x + 2$

answered Oct 29, 2020 at 17:36

4 votes

Accepted

How to calculate this scalar triple product?

answered Nov 7, 2020 at 15:07

4 votes

Accepted

The letters A B C D E are arranged randomly in a line. In how many arrangements is the letter A in front of D?

answered Nov 7, 2020 at 16:13

4 votes

Given $\angle A = 60°, \angle B = 80°, \angle C = 40°$, find $\alpha$

answered Nov 12, 2020 at 12:34

4 votes

Accepted

Simple proof of "maximum number of right angles in a convex $n$-gon is 3 for $n\geq 5$" for a 8th grade student?

answered Nov 22, 2020 at 18:36

4 votes

Accepted

Pythagoras Theorem Proof

answered Nov 29, 2020 at 20:37

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379 Answers

Easy way to see that $(x^2 + 5x + 4)(x^2 + 5x + 6) - 48 = (x^2 + 5x + 12)(x^2 + 5x - 2)$?

Where did I go wrong in applying the factor theorem?

Partition the remaining rectangle into equal parts.

Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.

Can $S_n=a_1a_2+a_2a_3+\cdots+a_na_1=0$ if $a_i=±1$ for $n=28$ and $n=30$?

(AIME 1994) $ \lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \ldots + \lfloor \log_2 n \rfloor = 1994 $

SMO problem: Sequence and series.

Finding angle in a triangle with one median and an isosceles triangle in it

Prove that the lines parallel to the angle bisectors through the midpoints of sides of a triangle are concurrent at the Spieker center

A problem related to $\int_{0}^{1} f(x)(x-f(x))dx=1/12$

Suppose $x$ and $y$ are unequal real numbers

Visual proof for $[\triangle ABC] = rs$?

summing this binomial series

Probability of lines in a pentagon intersecting internally or at vertices.

Exponent equation with common power

Finding solutions to $[x]^2 + 2[x]-3x=0$

Solve integral $\int\frac{1}{(x^2-1)\sqrt{x^2+1}}dx$

For which $n$, $n=x+y+xy$ has no solution in natural numbers?

How many rectangles can be found in this shape?

Let $P$ be a $30$-sided polygon inscribed in a circle. Find the value of $\frac{N}{100}$.

Four-letter words from the word MEDITERRANEAN such that the first letter is R and the fourth letter is E

Solve the inequality $x^4-3x^2+5\ge0$

Number of Dispersion Lines in A Square Dot Matrix

How to solve $x^2 \equiv 12 \pmod {13}$?

Factorizing $12x^3 - 8x^2 - 3x + 2$

How to calculate this scalar triple product?

The letters A B C D E are arranged randomly in a line. In how many arrangements is the letter A in front of D?

Given $\angle A = 60°, \angle B = 80°, \angle C = 40°$, find $\alpha$

Simple proof of "maximum number of right angles in a convex $n$-gon is 3 for $n\geq 5$" for a 8th grade student?

Pythagoras Theorem Proof