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Pen and Paper
  • Member for 2 years, 10 months
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17 votes
Accepted

Solve the equation $x^6-2x^5+3x^4-3x^2+2x-1=0$

5 votes

Why is $\sin\left[\arctan\left(\frac{x}{a}\right)\right] = \frac{x}{a\sqrt{\frac{x^2}{a^2} + 1}}$ true?

3 votes
Accepted

Prove that: $\sum_{i=1}^{5}x_i\sum_{i=1}^{5}\frac {1}{x_i}\leq 25$

3 votes
Accepted

Find all roots of $p(z)=z^6+z^3-6$

2 votes
Accepted

Prove $\frac{1}{u_{0} u_{1}}+\frac{1}{u_{1} u_{2}}+\ldots+\frac{1}{u_{i} u_{i+1}}+\ldots \ldots+\frac{1}{u_{n} u_{n+1}}=\frac{n+1}{u_{0} u_{n+1}}$

2 votes

Need help on remainder factor theorem question.

2 votes

How to evaluate an integral that comes out as undefined

1 vote
Accepted

How to find the number of ways seven boys and three girls can be seated in a row if the girls sit together at one end of the row

1 vote

Interval to the integral $y=f(x)=\int e^{\frac{x}{2}}\sin\left(\frac{\sqrt{3}}{2}x\right)$ when $x\leq 0$

1 vote
Accepted

How to calculate Integral of sine raised to the power of $2l+1$

0 votes
Accepted

Probability of losing at least K consecutive games after N games

0 votes

How to prove in any $△ABC$ that if $∠B$ is acute, then $c > b \cdot \cos A$?