The number of the integral solution of the equation(x+1)^2+(y-2)^_数学解答

The number of the integral solution of the equation(x+1)^2+(y-2)^2=50 is

人气：476 ℃　时间：2020-04-14 07:53:19

解答

小于50的完全平方数只有0,1,4,9,16,25,36,49.
两个完全平方数之和为50只有1+49 = 25+25 = 49+1三种可能.
于是(x+1)²+(y-2)² = 50的整数解有:
(0,9),(0,-5),(-2,9),(-2,-5),(4,7),(4,-3),(-6,7),(-6,-3),(6,3),(6,1),(-8,3),(-8,1).
共12组.