List questions from algebra-precalculus

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When are the Laws of Exponents correct?

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Simplification of radicals: $\sqrt{4+\sqrt5}-\sqrt{\frac{4+\sqrt{11}}{2}}$

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Intersection of two planes on a line

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Solving for variable inside rational root

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For which $a\in\mathbb{R}, \lim \limits_{x \to a}$ of given function exist?

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Does $\exp(\sum_i a_i \log(a_i)) = \prod_i a_i^{a_i}$?

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Behaviour of a function in two variables

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Solve $\frac{x^2}{\left(a+\sqrt{a^2+x^2}\right)^2}+\frac{x^2(1+x^2)}{\left(a+\sqrt{a^2+x^2(1+x^2)} \right)^2}=1$

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Why is $\sum_\limits{k=1}^{n}\sum_\limits{j=1}^{k}j = \frac12\left(\sum_\limits{k=1}^{n}k^2+\sum_\limits{k=1}^{n}k\right)$

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Solve $\frac{1}{x} \neq \frac{1}{x}$

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Upper bound on real roots of depressed cubic

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Is there a way to solve a very complicated equation in one variable?

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A few questions about basic algebra.

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Exponent log inequalites

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Black and white balls probability

When are the Laws of Exponents correct?

Simplification of radicals: $\sqrt{4+\sqrt5}-\sqrt{\frac{4+\sqrt{11}}{2}}$

Intersection of two planes on a line

Solving for variable inside rational root

For which $a\in\mathbb{R}, \lim \limits_{x \to a}$ of given function exist?

Does $\exp(\sum_i a_i \log(a_i)) = \prod_i a_i^{a_i}$?

Behaviour of a function in two variables

Solve $\frac{x^2}{\left(a+\sqrt{a^2+x^2}\right)^2}+\frac{x^2(1+x^2)}{\left(a+\sqrt{a^2+x^2(1+x^2)} \right)^2}=1$

Why is $\sum_\limits{k=1}^{n}\sum_\limits{j=1}^{k}j = \frac12\left(\sum_\limits{k=1}^{n}k^2+\sum_\limits{k=1}^{n}k\right)$

Solve $\frac{1}{x} \neq \frac{1}{x}$

Upper bound on real roots of depressed cubic

Is there a way to solve a very complicated equation in one variable?

A few questions about basic algebra.

Exponent log inequalites

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