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换元法即是在解题时,把某个式子看成一个整体,用一个变量去替换它,这样使问题得到简化.换元的实质就是转化,关键是构造元和设元,理论依据是等量代换,将复杂的研究对象转化成简单、熟悉的对象;将分散的条件联系起来,隐含地条件显露出来;或变为熟悉的形式,把复杂的计算和推证简化.它可将高次化为低次,化低次为高次,化分式为整式,化无理式为有理式,化超越式为代数式;在研究方程、不等式、函数、数列、三角等问题中都有广泛的应用.换元的方法有局部换元(又称整体换元,是在已知或未知中,某个代数式几次出现,而用一个字母来代替它从而简化问题)、三角换元(应用于去根
The method of changing yuan is to solve a problem, take a formula as a whole, and replace it with a variable, so that the problem can be simplified. The essence of changing a dollar is transformation. The key is constructing yuan and setting yuan, the theoretical basis Is the equivalent substitution, the complex object of study into a simple, familiar object; the scattered conditions associated with the implicit conditions revealed; or into a familiar form, the complex calculation and simplification of the deduction it We can change the high order into the low order, the low order to the higher order, the fraction into the whole form, the irrational form into the rational form and the transcendental form to the algebraic form. In the research equation, inequality, function, number sequence and triangle There are a wide range of applications.Transformation of the method of partial replacement (also known as the overall replacement, is known or unknown, an algebraic several times appear, and use a letter instead of it to simplify the problem), Triangle yuan (Applied to the root