List questions from problem-solving

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How does $\left(p+\frac{2-p^2}{r}\right)^2<2$ simplify to $2pr+2-p^2<r^2$?

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List Question

I have an equation like ax + by + cz = 0, where a, b, c are constants, I need to find x, y, z

Find the green area

How does $\left(p+\frac{2-p^2}{r}\right)^2<2$ simplify to $2pr+2-p^2<r^2$?

How to compute a minimal spanning set and the minimal spanning number of $\Bbb C[x,y]_{(x-1,y-1)}/(x^3-y^2)$?

how to epsilon-delta

What is the simplest way to approach this integral problem? To me, this problem seemed to necessitate some kind of gimmick.

How one can notice when a famous formulas is extended?

solution using symmetry to probability question involving 3 jurors

Expected Value Question 30 sided/20 sided die solution Issue

Determination of the basis angle in a tilted equilateral triangle

Interesting Card game Problem

Question About Half-Open Cubes on $\mathbb{R}^d$

Determinant of $n \times n$ matrix of a sort of skew symmetric matrix plus some diagonal

Polar coordinate system : Is radial coordinate is a function of angular coordinate?

Making up groups of Coins

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