Biquadratic equation, solution of biquadratic equations

Everyone from the school knows such a notion asequations. An equation is an equation containing one or more variables. Knowing that one of the parts of the given equality is equal to the other, it is possible to isolate individual parts of the equation, transferring some of its components for an equal sign according to clearly stipulated rules. It is possible to simplify the equation to the necessary logical conclusion in the form x = n, where n is any number.

From elementary school all children undergo a course of studylinear equations of various complexity. Later, more complex linear equations appear in the program-square, then cubic equations. Each subsequent form of equations has new solution techniques, it becomes more difficult to study and repeat.

However, after this a question arises about the solutionThis kind of equations, such as biquadratic equations. This kind, despite the seeming complexity, is solved quite simply: the main thing is to be able to bring such equations into the proper form. Their solution is studied in one or two lessons together with practical assignments, if students have a basic knowledge of the solution of quadratic equations.

What do you need to know the person who is confronted withby this type of equations? To begin with, they include only the even powers of the variable "X": the fourth and, respectively, the second. For a biquadratic equation to be solved, it is necessary to bring it to the form of a quadratic equation. How to do it? Simple enough! You just need to replace the "X" in the square with the "york". Then the awesome "X" for many schoolchildren in the fourth degree will turn into a "gambler" in a square, and the equation will look like an ordinary square one.

Further, it is solved as an ordinary squarethe equation is decomposed into multipliers, after which the meaning of the mysterious "game" is found. To solve the biquadratic equation to the end, it is necessary to find the square root of the "game" number - this is the required value of "x", after finding the values ​​of which you can congratulate yourself on the successful completion of calculations.

What should be remembered when solving the equations of thiskind? First and foremost, the game can not be a negative number! The very condition that the game is a square of the number X excludes a similar solution. Therefore, if at the primary solution of the biquadratic equation one of the values ​​of "gambler" turns out to be positive, and the second - negative, it is necessary to take only its positive variant, otherwise the biquadratic equation will be decided incorrectly. It is better to immediately enter the rule that the variable "igrok" is greater than or equal to zero.

The second important nuance: the number "x", being the square root of the "game" number, can be either positive or negative. Let's say that if the "game" is four, then the biquadratic equation will have two solutions: two and minus two. This is because the negative number raised to an even power is equal to the number of the same module, but different sign, raised to the same degree. Therefore, it is always worth remembering this important moment, otherwise you can simply lose one or more answers to the equation. It is best to write at once that "X" is equal to plus or minus the square root of "igruk".

In general, the solution of biquadratic equations -it is quite simple and does not require a lot of time. To study this topic in the school curriculum, two academic hours are enough - not counting, of course, repetitions and tests. Biquadratic equations of the standard form are very easily solved if the rules listed above are observed. Their solution will not be difficult for you, because it is detailed in the textbooks of mathematics. Successful study and success in solving any mathematical problems!