User Bowei Tang - Mathematics Stack Exchange

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Given $\alpha$ and $\beta$ are roots of the equation $x^2-5x+2=0$ then $\frac{4\alpha+\beta^5}{5\beta^2}=?$

May 7

How to evaluate $\int \frac{x^9}{(4x^2 + 1)^6}\mathrm dx$?

Mar 6

Confusion about Mathematical Induction

Jul 29, 2024

Find all integer values of $a$ such that the equation $(a+1)x^2 - (a^2+1)x + 2a^3 - 6 = 0$ has at least one integer root.

Jan 27

Which one of these books is better for abstract algebra to help build a strong foundation for advanced-level algebraic topology?

Jun 4, 2024

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Calculate the ideal class group of $K=\mathbb{Q}(\sqrt[3]{11})$

Jul 10, 2024

Understanding Freyd's Theorem in Category Theory

Jun 14, 2024

$a+b\sqrt{2}>1, a^2-2b^2=\pm 1 (a,b\in \mathbb{Z}) \implies a+b\sqrt {2}\geq 1+\sqrt {2}$

Jul 15, 2024

Find a fundamental unit by using the continued fraction

Jul 9, 2024

Compute $\int_C\frac{z^{2011}}{z^{2011}+z^{2010}+z^{2009}+1}dz$ with two different answers

Dec 6, 2024

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+10

Holder inequality is equality for $p =1$ and $q=\infty$

+40

Doubt on a proof that $\sin(t)$, $\cos(t)$, and $t$ are linearly independent in the vector space of functions from $\mathbb{R}$ to $\mathbb{R}$

+35

Range of base $a$ such that $f(x) = a^x - bx + e^2$ has two distinct zeros for all $b > 2e^2$

+15

The quadratic equation $x^2 - (c+3)x + 9 = 0$ has real roots $x_1$ and $x_2$. If $x_1 < -2$ and $x_2 < -2$, find value of $c$.

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