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This'll be a doozy

Let \(a\) and \(b\) be given real numbers. Solve the system of equations

\[\frac {x - y \sqrt {x^2 - y^2}}{\sqrt {1 - x^2 + y^2}} = a,\]

\[\frac {y - x \sqrt {x^2 - y^2}}{\sqrt {1 - x^2 + y^2}} = b\]

for real numbers \(x\) and \(y\).

Note by Sharky Kesa
2 years, 7 months ago

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Nice problem!

Solutions:

\(x= \dfrac{a+b\sqrt{m}}{\sqrt{1-m}}\) and \(y= \dfrac{b+a\sqrt{m}}{\sqrt{1-m}}\),where \(m = a^2 -b^2\) Harsh Shrivastava · 4 months ago

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@Harsh Shrivastava I can't even remember the answer. 2 years 3 months ago!!! Sharky Kesa · 4 months ago

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@Sharky Kesa Source of the problem?? Harsh Shrivastava · 4 months ago

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@Sharky Kesa Oh NP, I'll post full solution when I m free. Harsh Shrivastava · 4 months ago

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