Everyone from school is a concept known as the equation.Equation - equality containing one or more variables.Knowing what part of this equation is equal to the other, it is possible to isolate parts of the equation, transferring certain of its components for the equal sign on clearly defined rules.Equation can be simplified to complete the necessary logic in the form x = n, where n - is any integer.
From primary school, all children are treated with the study of linear equations of varying complexity.Later in the program appear more complex linear equations - the square, followed by the cubic equation.Each subsequent form of the equations is a new technique solutions, it becomes more difficult to learn and repeat.
But then the question arises of solving this type of equation as biquadratic equation.This view, in spite of the apparent complexity, dares simply enough: the main thing - to be able to lead such equations in proper form.Their decision to study for one or two lessons together with practical tasks, if students have a basic knowledge about solving quadratic equations.
What you need to know a person, faced with this type of equations?To begin with the fact that they include only even powers of the variable "X": fourth and respectively second.To biquadratic equation was solved, it is necessary to bring it into the form of a quadratic equation.How to do it?Simple enough!You just replace the "X" in the box on the "y".Then intimidating for many students "X" in the fourth degree turn into a "y" in the square, and the equation becomes an ordinary square.
Next, it is decided as an ordinary quadratic equation: decomposed into factors, then the value is the mysterious "y."To solve biquadratic to the end, you need to find the square root of the number of "y" - this is the unknown quantity "X", after finding the values of which can congratulate themselves on the successful completion of calculations.
What must be remembered, solving equations of this type?First and foremost: y can not be a negative number!The very condition that y - is the square of the number of X eliminates this type of solution.Therefore, if the primary decision biquadratic equation one of the values "y" turns out you have a positive, and the second - no, it is necessary to take only positive option, or biquadratic equation is solved false.It is better to introduce a rule that the variable "y" is greater than or equal to zero.
second important thing: the number of "X", as the square root of the number of "y" can be both positive and negative.For example, if "y" is equal to four, the biquadratic equation will have two solutions: two and minus two.This occurs because the negative number raised to an even power, equal to the number of the same module, but other than the mark, raised to the same degree.Therefore it is always worth remembering on this important point, otherwise you can just lose one or more of the responses of the equation.It is best to write that "X" is equal to plus or minus the square root of the "y".
In general, the decision to biquadratic equations - it is quite simple and does not require time-consuming.In the study of this subject in the school curriculum missing two academic hours - not counting, of course, repetition and control works.Biquadratic standard form are solved very easily if you follow the above rules.Their decision will not be any work for you, because it is painted in detail in textbooks of mathematics.Good luck with your studies and in solving any success, not only mathematical, problems!
