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x^2-y^2=100,且x,y为整数,求x,y.
题目详情
x^2-y^2=100,且x,y为整数,求x,y.
▼优质解答
答案和解析
x^2-y^2=100
(x+y)(x-y)=100=2×50=10×10
由于x+y与x-y同奇同偶
所以
x+y=50,x-y=2
或x+y=-50,x-y=-2
或x+y=10,x-y=10
或x+y=-10,x-y=-10
共四组解
(x+y)(x-y)=100=2×50=10×10
由于x+y与x-y同奇同偶
所以
x+y=50,x-y=2
或x+y=-50,x-y=-2
或x+y=10,x-y=10
或x+y=-10,x-y=-10
共四组解
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