Logic Equations

Christian Posthoff and Bernd Steinbach
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Christian Posthoff: The University of The West Indies
Bernd Steinbach: Freiberg University of Technology

Chapter Chapter 3 in Logic Functions and Equations, 2004, pp 91-100 from Springer

Abstract: Abstract For an easy access to these concepts we will go back to the basic understanding of an equation, as it is known from elementary mathematics. An equation ax+ b = c or ax 2 + bx + c = d is a constraint for the values of x, and a solution x 1 allows the transformation of the equations in the identities c = c by calculating ax 1 + b which results in c or by calculating ax 1 2 + bx 1 + c that has to result in d. It is well known that these equations are equivalent to the equations ax + (b - c) = 0 or ax 2 + bx + (c - d) = 0 (i.e. these equations have the same solutions as the original equations) . Further transformations result in $$x + \frac{{b - c}}{a} = 0$$ or $${x^2} + \frac{b}{a}x + \frac{{c - d}}{a} = 0$$ which can be changed to x + x 0 = 0 or x 2 + px +q = 0, and the solutions are $$x = - {x_0}\quad {x_{1,2}} = - \frac{p}{2} \pm \sqrt {\frac{{{p^2}}}{4} - q,} $$ , under consideration of several conditions, like $$a \ne 0,\frac{{{p^2}}}{4} - q \geqslant 0$$ .

Date: 2004
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DOI: 10.1007/978-1-4020-2938-7_3

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