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
4 years, 3 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 $$m = a^2 -b^2$$

- 2 years ago

I can't even remember the answer. 2 years 3 months ago!!!

- 2 years ago

Source of the problem??

- 2 years ago

Oh NP, I'll post full solution when I m free.

- 2 years ago