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The methods for solving equations generally depend on the type of equation, both the kind of expressions in the equation and the kind of values that may be assumed by the unknowns. The variety in types of equations is large, and so are the corresponding methods.
This counterintuitive result occurs because in the case where =, multiplying both sides by multiplies both sides by zero, and so necessarily produces a true equation just as in the first example. In general, whenever we multiply both sides of an equation by an expression involving variables, we introduce extraneous solutions wherever that ...
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...
Illustrations in Jade Mirror of the Four Unknowns Jia Xian triangle. Jade Mirror of the Four Unknowns, [1] Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, [2] is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. [3]
This does not reduce the generality, as this can be realized by subtracting the right-hand side from both sides. The most common type of equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials. The sides of a polynomial equation contain one or more terms. For example, the equation
For the spherical case, one can first compute the length of side from the point at α to the ship (i.e. the side opposite to β) via the ASA formula = (+) + (), and insert this into the AAS formula for the right subtriangle that contains the angle α and the sides b and d: = = + . (The planar ...
The "I Have 6 Eggs" riddle has gone viral across social media, puzzling many with its deceptively easy setup. Despite its basic premise of just counting some eggs, this riddle has proven a bit ...
Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves , algebraic surfaces , or, more generally, algebraic sets , their study is a part of algebraic geometry that is called Diophantine geometry .