Newbetuts

On solving $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+x}}}}=\sqrt[3]{6+\sqrt[3]{6+\sqrt[3]{6+\sqrt[3]{6+x}}}}$

What remainder does $34!$ leave when divided by $71$?

About rationalizing expressions

Polynomial maximization: If $x^4+ax^3+3x^2+bx+1 \ge 0$, find the maximum value of $a^2+b^2$

Significance of multiplying $-1$ by $-1$

Prove the following (algebra of polynomials)

What's $(-1)^{2/3}\; $?

Under what conditions does $x^{\frac{b}{c}} = (x^b)^\frac{1}{c}$ hold?

For $(x+\sqrt{x^2+3})(y+\sqrt{y^2+3})=3$, compute $x+y$ .

Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals

Interesting relation derived from the identity $\sin^2 x + \cos^2 x \equiv 1$

If $A^2+B^2=C^2$ with $A$ odd, $A,B,C$ coprime and $A<B<C$, is $B+C$ a square? [closed]

Interval of monotonicity of the function $f(x)=\frac{\ln (\pi+x)}{\ln (e+x)}$

what does $|x-2| < 1$ mean?

Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$

Every year, there is a contest...

Which of the integers cannot be formed with $x^2+y^5$

New posts in algebra-precalculus

How many distinct ways are there to $2$-color the $8$ vertices of a cube?

Closed-Form Solution to Infinite Sum

find $\left( \frac{x}{x+y} \right)^{2007} + \left( \frac{y}{x+y} \right)^{2007}$

On solving $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+x}}}}=\sqrt[3]{6+\sqrt[3]{6+\sqrt[3]{6+\sqrt[3]{6+x}}}}$

What remainder does $34!$ leave when divided by $71$?

About rationalizing expressions

Polynomial maximization: If $x^4+ax^3+3x^2+bx+1 \ge 0$, find the maximum value of $a^2+b^2$

Significance of multiplying $-1$ by $-1$

Prove the following (algebra of polynomials)

What's $(-1)^{2/3}\; $?

Under what conditions does $x^{\frac{b}{c}} = (x^b)^\frac{1}{c}$ hold?

For $(x+\sqrt{x^2+3})(y+\sqrt{y^2+3})=3$, compute $x+y$ .

Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals

Interesting relation derived from the identity $\sin^2 x + \cos^2 x \equiv 1$

If $A^2+B^2=C^2$ with $A$ odd, $A,B,C$ coprime and $A<B<C$, is $B+C$ a square? [closed]

Interval of monotonicity of the function $f(x)=\frac{\ln (\pi+x)}{\ln (e+x)}$

what does $|x-2| < 1$ mean?

Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$

Every year, there is a contest...

Which of the integers cannot be formed with $x^2+y^5$