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中学教材中,解根式方程的常用方法是通过方程两边乘方使方程有理化。但是,对于一些特殊的根式方程,如果盲目乘方,往往会招致繁琐的计算,甚至达不到化为有理方程的目的。这就需要注意题中所隐含的一些特殊条件,用以达到简化解题过程的目的。举例于下: 例1 解方程(2x+3)~(1/2)-(x+1)~(1/2)++(3x-5)~(1/2)-(4x-3)~(1/2)=0。解本题如盲目地移项乘方,,可能招致繁琐运算。若注意到第一、三项的平方和等于第二、四项的平方和这一隐含条件,将二、四项移至右边,方程两边平方后,消去
In the middle school textbooks, the common method of solving the root equation is to rationalize the equation by using the two sides of the equation. However, for some special root equations, blind power will often lead to tedious calculations, and it will not even achieve the purpose of rationalizing the equation. This requires attention to the special conditions implied in the questions to simplify the problem solving process. Examples are as follows: Example 1 Solution Equation (2x+3)~(1/2)-(x+1)~(1/2)++(3x-5)~(1/2)-(4x-3) ~(1/2)=0. Solving this problem, such as blindly shifting items, may incur tedious calculations. If you notice that the sum of the squares of the first and third terms is equal to the implied condition of the sum of the squares of the second and fourth terms, move the second and fourth terms to the right. After the two sides of the equation are squared, eliminate