题在补充说明那里要过程X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,y为根号N+1 + 根号N 分之根号N+1 - 根号,N为自然数,2X^2+197xy+2y^2 = 1993 成立 N为
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![题在补充说明那里要过程X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,y为根号N+1 + 根号N 分之根号N+1 - 根号,N为自然数,2X^2+197xy+2y^2 = 1993 成立 N为](/uploads/image/z/10189250-26-0.jpg?t=%E9%A2%98%E5%9C%A8%E8%A1%A5%E5%85%85%E8%AF%B4%E6%98%8E%E9%82%A3%E9%87%8C%E8%A6%81%E8%BF%87%E7%A8%8BX%3D%E6%A0%B9%E5%8F%B7N%2B1+-+%E6%A0%B9%E5%8F%B7N+%E5%88%86%E4%B9%8B+%E6%A0%B9%E5%8F%B7N%2B1+%2B+%E6%A0%B9%E5%8F%B7N+%2Cy%E4%B8%BA%E6%A0%B9%E5%8F%B7N%2B1+%2B+%E6%A0%B9%E5%8F%B7N+%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B7N%2B1+-+%E6%A0%B9%E5%8F%B7%2CN%E4%B8%BA%E8%87%AA%E7%84%B6%E6%95%B0%2C2X%5E2%2B197xy%2B2y%5E2+%3D+1993+%E6%88%90%E7%AB%8B+N%E4%B8%BA)
题在补充说明那里要过程X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,y为根号N+1 + 根号N 分之根号N+1 - 根号,N为自然数,2X^2+197xy+2y^2 = 1993 成立 N为
题在补充说明那里
要过程
X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,y为根号N+1 + 根号N 分之根号N+1 - 根号,N为自然数,2X^2+197xy+2y^2 = 1993 成立 N为
题在补充说明那里要过程X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,y为根号N+1 + 根号N 分之根号N+1 - 根号,N为自然数,2X^2+197xy+2y^2 = 1993 成立 N为
先进行分母有理化:
X=根号N+1 - 根号N 分之 根号N+1 + 根号N ,
=(根号N+1 +根号N)^2
=N+1+2根号(N+1)N+N
=2N+1+2根号(N+1)N
y=根号N+1 + 根号N 分之根号N+1 - 根号N
=(根号N+1 -根号N)^2
=2N+1-2根号(N+1)N
2X^2+197xy+2y^2 = 1993
2(x^2+2xy+y^2)+193xy=1993
2(x+y)^2+193xy=1993
2(4N+2)^2+193(N+1-N)^2=1993
2*4(2N+1)^2+193=1993
(2N+1)^2=225
2N+1=15
N=7