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这是现行初中代数教材上的一道习题: 解关于x的方程 (a-x)~(1/2)(x-b)~(1/2)=(a-b)~(1/2)(A) 限制在条件a≥b,b≤x≤a下,将(A)两边平方,得 2(a-x)(x-b)~(1/2)=0。方程的两根是x=a或x=b。研究了(A)型方程的特点后来解这类无理方程是相当简捷的.现举数例如下。例1 解方程(100-x)~(1/2)+(x-64)~(1/2)=6。解:将原方程化为(A)型:
This is an exercise in the current junior high school algebra textbook: Solution for x (ax) ~ (1/2) (xb) ~ (1/2) = (ab) ~ (1/2) (A) When a≥b and b≤x≤a, (A) is squared on both sides to obtain 2(ax)(xb)~(1/2)=0. The two roots of the equation are x=a or x=b. It is fairly straightforward to study the characteristics of (A) equations to solve these irrational equations. Example 1 Solution equation (100-x)~(1/2)+(x-64)~(1/2)=6. Solution: Turn the original equation into type (A):