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已知:a+b=根号2010+根号2009的正平方根,a-b=根号2010-根号2009的正平方根,求(a乘b)平方的值.
人气:374 ℃ 时间:2020-03-26 09:29:23
解答
a+b = √{√2010+√2009}
a-b = √{√2010-√2009}
ab = 1/4{(a+b)²-(a-b)²} = 1/4{(√2010+√2009)-(√2010-√2009)} = 1/4×2√2009 = 1/2×√2009
(ab)² = {1/2×√2009}² = 2009/4
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