Newbetuts

$x+ay=4, ax+9y=b$, Find the values of $a$ and $b$ for which the system has more than one set of solutions

Eliminate $\theta$ from the equations $\frac{\cos(\alpha-3\theta)}{\cos^3\theta}=\frac{\sin(\alpha-3\theta)}{\sin^3\theta}=m$

The inequality $\,2+\sqrt{\frac p2}\leq\sum\limits_\text{cyc}\sqrt{\frac{a^2+pbc}{b^2+c^2}}\,$ where $0\leq p\leq 2$ is: Probably true! Provably true?

Challenging inequality: $abcde=1$, show that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e}+\frac{33}{2(a+b+c+d+e)}\ge{\frac{{83}}{10}}$

Finding the real solutions to $16^{x^{2} + y } + 16^{y^{2}+ x} = 1$

Is my method of solving equation correct?

Is my work transforming $9(x+2)^2$ to $(3x+6)^2$ correct? What is this method called?

Assume $\alpha, \beta \in \Bbb C,$ such that $\alpha^m = \beta^n = 1$ show that $(\alpha+\beta)^{mn}\in \Bbb R$

Eliminate $t$ from $h=\frac{3t^2-4t+1}{t^2+1}, k=\frac{4-2t}{t^2+1}$

Can there be integer solutions (please PROVE) [closed]

Simplification of a sum of Bessel functions

how to compare $\sin(19^{2013}) $ and $\cos(19^{2013})$

A question about the definition of polynomials.

Recurrence relation: $a_n = 3a_{n-1} + 2n, a_0 = 1$

Calculation of $x$ in $x \lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor = 88$

$x=\sqrt[3]{\sqrt{5}+2}+\sqrt[3]{\sqrt{5}-2}$ is rational or irrational?

Root or zero...which to use when?

New posts in algebra-precalculus

Walk through on Distributive Property Discrete Mathematics Problem

If $x = \frac{\sqrt{111}-1}{2}$, calculate $(2x^{5} + 2x^{4} - 53x^{3} - 57x + 54)^{2004}$.

What is the standard interpretation of order of operations for the basic arithmetic operations?

$x+ay=4, ax+9y=b$, Find the values of $a$ and $b$ for which the system has more than one set of solutions

Eliminate $\theta$ from the equations $\frac{\cos(\alpha-3\theta)}{\cos^3\theta}=\frac{\sin(\alpha-3\theta)}{\sin^3\theta}=m$

The inequality $\,2+\sqrt{\frac p2}\leq\sum\limits_\text{cyc}\sqrt{\frac{a^2+pbc}{b^2+c^2}}\,$ where $0\leq p\leq 2$ is: Probably true! Provably true?

Challenging inequality: $abcde=1$, show that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e}+\frac{33}{2(a+b+c+d+e)}\ge{\frac{{83}}{10}}$

Finding the real solutions to $16^{x^{2} + y } + 16^{y^{2}+ x} = 1$

Is my method of solving equation correct?

Is my work transforming $9(x+2)^2$ to $(3x+6)^2$ correct? What is this method called?

Assume $\alpha, \beta \in \Bbb C,$ such that $\alpha^m = \beta^n = 1$ show that $(\alpha+\beta)^{mn}\in \Bbb R$

Eliminate $t$ from $h=\frac{3t^2-4t+1}{t^2+1}, k=\frac{4-2t}{t^2+1}$

Can there be integer solutions (please PROVE) [closed]

Simplification of a sum of Bessel functions

how to compare $\sin(19^{2013}) $ and $\cos(19^{2013})$

A question about the definition of polynomials.

Recurrence relation: $a_n = 3a_{n-1} + 2n, a_0 = 1$

Calculation of $x$ in $x \lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor = 88$

$x=\sqrt[3]{\sqrt{5}+2}+\sqrt[3]{\sqrt{5}-2}$ is rational or irrational?

Root or zero...which to use when?