Everyone else from school knows such a thing as equations. An equation is an equality containing one or more variables. Knowing that one of the parts of this equality is equal to the other, it is possible to isolate the individual parts of the equation, transferring one or another of its components as an equal sign according to clearly defined rules. You can simplify the equation to the necessary logical conclusion in the form x = n, where n is any number.
From elementary school, all children take a course of studying linear equations of varying complexity. Later, more complex linear equations appear in the program - quadratic ones, then cubic equations follow. Each subsequent type of equations has new methods of solution, it becomes more difficult to study and repeat.
However, after this the question arises of solving such a type of equation as biquadratic equations. This type, despite the apparent complexity, is solved quite simply: the main thing is to be able to bring such equations into proper form. Their solution is studied in one or two lessons, along with practical tasks, if students have basic knowledge about solving quadratic equations.
What does a person who is faced with this type of equations need to know? To begin with, the fact that they include only the even degrees of the variable “x”: the fourth and, accordingly, the second. For the biquadratic equation to be solved, it is necessary to bring it to the form of a quadratic equation. How to do it? Simple enough! It is only necessary to replace the "X" in the square with the "game". Then the intimidating “X” for many students will turn into a “square” in the fourth degree, and the equation will take the form of a normal square.
Then it is solved as an ordinary quadratic equation: decomposed into factors, after which the meaning of the mysterious "game" is found. To solve the biquadratic equation to the end, you need to find the square root of the number “igrek” - this will be the desired value “x”, after finding the values of which you can congratulate yourself on the successful completion of the calculations.
What should be remembered when solving equations of this type? First and foremost: a game cannot be a negative number! The very condition that the game is the square of the x-number excludes a similar solution. Therefore, if during the initial solution of the biquadratic equation one of the “game” values turns out to be positive and the second negative, you need to take only its positive variant, otherwise the biquadratic equation will be solved incorrectly. It’s better to immediately introduce the rule that the player ’variable is greater than or equal to zero.
The second important nuance: the number “X”, being the square root of the number “game”, can be both positive and negative. Suppose 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 degree is equal to the number of the same module, but a different sign raised to the same degree. Therefore, it is always worth remembering this important point, otherwise you can simply lose one or more answers of the equation. It is best to immediately write that “X” is equal to plus or minus the square root of the “game”.
In general, solving biquadratic equations is quite simple and does not require a lot of time. Two academic hours are enough to study this topic in the school curriculum - not counting, of course, repetitions and tests. Standard-type biquadratic equations are solved very easily if the above rules are observed. Their solution will not be difficult for you, because it is described in detail in the textbooks of mathematics. Good luck with your studies and success in solving any, not just mathematical, problems!