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GAVD's user avatar
GAVD's user avatar
GAVD
  • Member for 8 years, 9 months
  • Last seen this week
  • Somewhere on earth
40 votes

Square root confusion: Why am I getting an answer if it doesn't work?

13 votes
Accepted

The probability that A hits a target is $\frac14$ and that of B is $\frac13$. If they fire at once and one hits the target, find $P(\text{A hits})$

9 votes
Accepted

Proving roots of a polynomial are real and distinct.

9 votes

Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too

9 votes

Is the subset of squares of a group a subgroup?

8 votes

Why is the matrix product of 2 orthogonal matrices also an orthogonal matrix?

8 votes
Accepted

Verifying that the Sequence $\frac{4n-1}{5n}$ is Bounded and Increasing

8 votes
Accepted

Calculate eigenvalues and eigenvectors

8 votes
Accepted

Proving $f(x)>0$ on $\mathbb{R}^+$ given that $f(0)=0$ and $f'(x)>f(x)$

8 votes

$x^2 + 3x + \frac{3}x + \frac{1}{x^2} = 26$ and $x$ can be written as $a + \sqrt{b}$ where $a$ and $b$ are positive integers, then find $a + b$.

7 votes
Accepted

For $0<x<\dfrac{\pi}{4}$ prove that $\frac{\cos x}{\sin^2x(\cos x-\sin x)}>8$.

7 votes
Accepted

If $a,b,c$ are positive reals, then prove that $(a+b)(a+c)\ge 2 \sqrt {abc(a+b+c)}$

7 votes
Accepted

How to prove $\sum _{k=1}^{\infty} \frac{k-1}{2 k (1+k) (1+2 k)}=\log_e 8-2$?

7 votes

Proving that $\frac{\sin \alpha + \sin \beta}{\cos \alpha + \cos \beta} =\tan \left ( \frac{\alpha+\beta}{2} \right )$

7 votes

Find all polynomials $p$ such that $p(x+1)=p(x)+2x+1.$

6 votes

Prove that $\int_a^bxf(x)dx\geq\frac{b+a}{2}\int_a^bf(x)dx$

6 votes
Accepted

Prove that any two cyclic groups of the same order are isomorphic?

6 votes

What is the value of $\frac{a^2}{b+c} + \frac{b^2}{a+c} + \frac{c^2}{a+b}$ if $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 1$?

6 votes
Accepted

Simplifying $\tan100^{\circ}+4\sin100^{\circ}$

6 votes
Accepted

Simplifying $\sum_{i=1}^{n-2}i(n-1-i)$

6 votes
Accepted

Show by double counting that $ 3 {n \choose 4} + 3{n\choose 3} = {{n \choose 2} \choose 2}$

5 votes
Accepted

Given the matrix product $AB$ how can I determine the product $BA$

5 votes

let : $\forall n \in \mathbb{N}$ : $x_n=\sqrt{1+(1+1/n)^2}+\sqrt{1+(1-1/n)^2}$ then : $\displaystyle{\sum_{i=1}^{20}}\dfrac{1}{x_i}=?$

5 votes
Accepted

How to evaluate $45^\frac {1-a-b}{2-2a}$ where $90^a=2$ and $90^b=5$ without using logarithm?

5 votes

What Techniques of Integration would be best suited for this Integral?

5 votes

If $a,b,c\ge-1$ and $a^3+b^3+c^3=1$ prove $a+b+c+a^2+b^2+c^2\le4$

5 votes
Accepted

Evaluating $2x^3+2x^2-7x+72$ where $x= \frac{3-5i}{2} $

5 votes
Accepted

Find a formula for $\cos(5x)$ in terms of $\sin(x)$ and $\cos(x)$

4 votes

Proving that a group homomorphism preserves the identity element

4 votes
Accepted

construct triangle given angle and centroid

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