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小学数学四则运算中,除0+O=0x0,0-0=0x0,2+2=2X2外,通常情况下,两个数的和(差)与这两个数的积是不相等的。那么,在小数四则运算中,除以上特例外,是否还存在这样的两个数,使得它们的和(差)分别与它们的积相等?如果有,又有何规律?使用其规律能否为我们的有关计算带来简便?一、非零自然数中只有一组数对的和与积相等设两个非零自然数为a、b,要使它们的和与积相等,也就是求不定方程a+b=ab的正整数解,将原方程变形为(1/a)+(1/b)=1(※).当a=b=1时,显然不是
Primary school mathematics four operations, except for 0 + O = 0x0,0-0 = 0x0,2 +2 = 2X2, under normal circumstances, the sum of two numbers (difference) and the product of these two numbers are not equal. So, in the four decimal places, except for the above special cases, is there still such two numbers that make their sum (difference) equal to their product? If yes, what is the law? A simple nonzero natural number in which only one set of pairs of numbers is equal to the product of two nonzero natural numbers is a, b, so that their sum is equal to the product, that is, to find the indeterminate equation a + b = ab, the original equation is transformed into (1 / a) + (1 / b) = 1 (*). When a = b = 1, obviously not