Current location - Training Enrollment Network - Mathematics courses - The key process of mathematics competition in senior one.
The key process of mathematics competition in senior one.
Because the original equation has six natural number solutions, the original equation can be solved into three equations, each factor =0 (and they are different, that is, c 1, c2 and c3 are different; The relationship between the three equations is or). That is to say, each factor can be decomposed into the form of (x-a)(x-b) within the range of rational numbers (where A and B are the solutions of the original equation and are different natural numbers, satisfying a+b=6, ab=c 1, c2, c3). Therefore, according to natural numbers A and B, if a+b=6, we can get A, b=0 and 6 or 1 and 5 or 2 and 4. So c 1, c2 and c3 are both 0 or 5 or 8, so the maximum difference is 8-0=8.