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Partial Solution of Homework Assignment 1

this document in PDF: Sol01.pdf

Warning: The solutions presented here are partial at best. They are only intended for use as checks and hints and are often incomplete.

Question 1-11-ii: $ \{x: -5<x<11\}$.

Question 1-11-iv: $ \{x:  x<1$ or $ x>2\}$.

Question 1-11-vi: The empty set.

Question 1-11-viii: Same solutions as for $ (x-1)(x+2)=3$, which is a simple quadratic equation.

Question 1-12-iv: Replace $ y$ by $ -y$ in $ \vert x+y\vert\leq\vert x\vert+\vert y\vert$.

Question 1: Write $ ax^2+bx+c=a\left(x+\frac{b}{2a}\right)^2-\frac{b^2-4ac}{4a}$ and use the fact that $ \left(x+\frac{b}{2a}\right)^2$ is always positive (except for one value of $ x$).

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Dror Bar-Natan 2002-10-17