المپیاد ریاضی کشور ژاپن ; Japan Mathematics Olympiad

[@MrBahram1tiger]

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[@erfanmohagheghian707]

You are missing 2(out of 4) of the solutions. And that's because the +/- at the top do not necessarily coincide with the +/- at the bottom and you should keep them both and consider all the 4 cases. Here's the solution from Mathematica. I divided both sides by (a^2 * b^2) and set a/b = t and wrote the goal expression as (t+1)/(t-1) eq = t^2 + 1/t^2 == 10; sol = Solve[eq, {t}, Reals]; values = Table[(t + 1)/(t - 1) /. sol[[i]], {i, Length[sol]}]; N[values] {0.517638, -0.517638, -1.93185, 1.93185}