1. Kerimbekova M.S. MF-12 Equation

2. Equation is In mathematics, an equation is an equality containing one or more variables. The first use of an equals sign, equivalent to 14x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557).

3. The solution of the equation - the task of finding such values ​​ of the arguments, in which equality is achieved. Arguments specified functions (sometimes referred to as " variable " ) in the case of the equation are called "unknown." The values ​​ of the unknowns, in which equality is achieved, called the decisions or the roots of the equation.

4. Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector.

5. Types of equations Linear equations Quadratic equations Cubic equations Equation of the fourth degree Systems of the linear algebraic equations The equations with parameters Transcendental equations Functional equations Differential equations

6. The algebraic equation is called the look equation Algebraic equations

7. Differential equations So called equations containing one or more functions or their derivatives and differentials. Differential equations proved to be extremely valuable tool for the exact wording of the laws of nature.

8. Diophantine equations Diophantine equation called an algebraic equation with two or more unknowns with integer coefficients, the solution of which is sought in whole or rational numbers. For example, the equation 3x - 5y = 1 has a solution x = 7, y = 4 ; Generally, its decisions are integers of the form x = 7 + 5n, y = 4 + 3n.

9. The transcendental equation Equations that contain transcendental functions such as logarithmic, exponential, or trigonometric function, called transcendental. An example of the following equations are:

10. Integral Equations Equations containing unknown function under the integral sign, for example, f (s) = Tk (s, t) f (t) dt, where f (s) and K (s, t) are specified, and f (t) to be found.

11. Linear equations These simple equations are solved by reducing them to an equivalent equation, which shows the current value of the unknown. For example, the equation x + 2 = 7 can be reduced to an equivalent equation x = 5 by subtracting 2 from the right and left sides.

12. Linear equations Quadratic equations Cubic equations Equation of the fourth degree Systems of the linear algebraic equations

13. A task Mom bought apples and pears in the amount of 420 rubles. How many kilograms of apples bought Mom, if apples cost 30 rubles per kilogram, and pears - 120 rubles? Create and solve the task with the help of linear equations

14. Answer 30х + 120(х + 1) = 420. 30х + 120х + 120 = 420 150х + 120 = 420 150х = 420 - 120 150х = 300 х = 300 : 150 х = 2. So, my mother bought a 2 kg of apples.

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