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Word problems are another tool to show how algebra is applied to real-life situations. For example, students may be presented with a situation in which Naomi's brother has twice as many apples as Naomi. Given that both together have twelve apples, students are then asked to find an algebraic equation that describes this situation (+ =) and to ...
In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution .
All quadratic equations have exactly two solutions in complex numbers (but they may be equal to each other), a category that includes real numbers, imaginary numbers, and sums of real and imaginary numbers. Complex numbers first arise in the teaching of quadratic equations and the quadratic formula.
In mathematics, an algebraic equation or polynomial equation is an equation of the form =, where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and
Bernoulli's equation; Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations; Bessel's differential equation; Boltzmann equation; Borda–Carnot equation; Burgers' equation; Darcy–Weisbach equation; Dirac equation. Dirac equation in the algebra of physical space; Dirac–Kähler equation; Doppler equations; Drake equation (aka ...
In mathematics, a law is a formula that is always true within a given context. [1] Laws describe a relationship, between two or more expressions or terms (which may contain variables), usually using equality or inequality, [2] or between formulas themselves, for instance, in mathematical logic.
The primary algebra consists of equations, i.e., pairs of formulae linked by an infix operator '='. R1 and R2 enable transforming one equation into another. Hence the primary algebra is an equational formal system, like the many algebraic structures, including Boolean algebra, that are varieties.
Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes.
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