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商的算术平方根化成算式平方根的商是有条件限制的,即公式(a/b)~(1/2)=a~(1/2)/b~(1/2)仅当a≥0,b>0时才能成立.往往有同学忽视公式成立的条件,请看下面两道题:例1已知x+y=3,xy=2.求(x/y)~(1/2)+(y/x)~(1/2)的值.例2已知x+y=-3,xy=2.求(x/y)~(1/2)+(y/x)~(1/2)的值.这两题的结构相同,区別仅在于已知条件中两数和的符号相反,但是在解法上却是不一样的.
The quotient of the square root of the arithmetic square root of a business operator is conditionally restricted, that is, the formula (a / b) ~ (1/2) = a ~ (1/2) / b ~ b> 0 can often be established often have students ignore the conditions for the establishment of the formula, look at the following two questions: Example 1 Known x + y = 3, xy = 2. Find (x / y) ~ (y / x) ~ (1/2) .Example 2 It is known that x + y = -3 and xy = / 2) .These two questions have the same structure except that the sign of the two numbers sums in the known condition is opposite, but the solution is not the same.