奧數題 關於mod+solve equation 10分

Q2.
Let y = nx where n > 1
Sub. into the 1st equation
1/n^2x^2 + 1/nx^2 = 1
1/x^2 = n(1 - 1/n2) = (n^2 - 1)/n...............(1)
Sub. y = nx into the 2nd equation
n/x^2 + 1/n^3x^2 = 3
1/x^2 = 3n^3/(n^4 + 1) .....................(2)
From (1) and (2)
(n^2 - 1)/n = 3n^3/(n^4 + 1)
n^6 - 4n^4 + n^2 - 1 = 0
The only real and positive answer for n is 1.951
Sub this value into (1), we get x = 0.8338, y = nx = 1.6267.

Sub your solution to the question lead to different result. Can you check the question again?