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aarbee
  • Member for 8 years, 11 months
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11 votes
6 answers
5k views

Why every prime (>3) is represented as $6k\pm1$

10 votes
2 answers
772 views

Intuition for connectedness of positive definite matrices

8 votes
4 answers
35k views

Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd [closed]

7 votes
2 answers
5k views

Average of 3 consecutive odd numbers

7 votes
3 answers
11k views

$(x^{2022}+1)(1+x^2+x^4+...+x^{2020})=2022\cdot x^{2021}$

6 votes
2 answers
88 views

Solve for $x$: $\log_3(x-2)\ge\log_5(4-x)$

5 votes
2 answers
79 views

Let two subsets $P,Q$ be selected from the set $A=\{1,2,3,4,5\}$. Find the probability... [duplicate]

5 votes
2 answers
119 views

Finding the number of complex numbers satisfying $|z|=\text{max}\{|z-1|,|z+1|\}$

5 votes
4 answers
183 views

Find the range of $\frac{\sqrt{(x-1)(x+3)}}{x+2}$

5 votes
6 answers
26k views

Count of 3-digit numbers with at least one digit as 9

4 votes
1 answer
2k views

Cyclic subgroup of a quotient group

4 votes
4 answers
80k views

Common chord of two circles

4 votes
1 answer
585 views

Sum of two sets

4 votes
1 answer
7k views

Finding medians from vectors

4 votes
1 answer
75 views

Determining a sequence's $n$-th term from its first and second differences, when latter is in arithmetic or geometric progression

4 votes
1 answer
70 views

$a+b+c=-3\sqrt{ac}$

4 votes
2 answers
116 views

Domain of $7^{\log_7(x^2-4x+5)}$

4 votes
0 answers
80 views

Let $f(x)=\begin{cases}2x+a;&x\ge-1\\bx^2+3;&x\lt-1\end{cases}$ and $g(x)=\begin{cases}x+4;&0\le x\le4\\-3x-2;&-2\lt x\lt0\end{cases}$ then $g(f(x))$

4 votes
2 answers
91 views

Find the value of $\lim_{ n \to \infty} \left(\frac{1^2+1}{1-n^3}+\frac{2^2+2}{2-n^3}+\frac{3^2+3}{3-n^3}+...+\frac{n^2+n}{n-n^3}\right)$

4 votes
2 answers
120 views

Evaluate $\lim_{x\to(e^{-1})^+}\frac{e^{\frac{\ln(1+\ln x)}x}}{x-e^{-1}}$

3 votes
3 answers
101 views

Evaluate $\int_1^{\sqrt3}\left( x^{2x^2+1}+\ln x^{\left(2x^{2x^2+1}\right)}\right)dx$

3 votes
4 answers
96 views

If $\alpha\ne1,\alpha^6=1$ and $\sum_{r=1}^6 {^6}C_r\alpha^{r-1}=x,$ then find the value of $|x|$.

3 votes
1 answer
117 views

If $\cos\alpha+\cos\beta+\cos\gamma=\sin\alpha+\sin\beta+\sin\gamma=0$ and $\cos3\alpha=\dfrac34$ then find $\cos^8\alpha+\cos^8\beta+\cos^8\gamma$

3 votes
3 answers
125 views

The quadratic equation whose roots are $\sec^2\theta$ and $\csc^2\theta$ can be

3 votes
1 answer
78 views

If $f:R\to R$ satisfies $f(x+2xy)=f(x)+2f(xy)\forall x,y\in R$ and $f(10)=11$ then prove the following

3 votes
1 answer
55 views

Solve $\int\frac{a^2-x^2}{\sqrt{(a^2-x^2)^2-e^2}}dx$

3 votes
4 answers
542 views

Find the equations of circles passing through $(1, -1)$ touching the lines $4x+3y+5=0$ and $3x-4y-10=0$

3 votes
3 answers
127 views

If $x^3-\frac1{x^3}=108+76\sqrt2$, find $x-\frac1x$

3 votes
4 answers
209 views

A six digit number is formed randomly using digits $\{1,2,3\}$ with repetitions. Choose the correct option(s):

3 votes
1 answer
488 views

Finding $|A|^2+|B|^2$ if $A=\text{adj} (B)-B^T$ and $B=\text{adj} (A)-A^T$

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