Math Olympiad rational surd simultaneous equations

Solve simultaneous equations.
(x-ysqrt(x^2-y^2))÷(sqrt(1-x^2-y^2)) = 2 and other is
(y-xsqrt(x^2-y^2))÷(sqrt(1-x^2-y^2))= 7/4 .

Reply 1

Muttley79

Original post by alevelmath1

Solve simultaneous equations.
(x-ysqrt(x^2-y^2))÷(sqrt(1-x^2-y^2)) = 2 and other is
(y-xsqrt(x^2-y^2))÷(sqrt(1-x^2-y^2))= 7/4 .

Please post what you've tried as per forum guidelines

Reply 2

MindMax2000

Universities Forum Helper

Original post by alevelmath1

Solve simultaneous equations.
(x-ysqrt(x^2-y^2))÷(sqrt(1-x^2-y^2)) = 2 and other is
(y-xsqrt(x^2-y^2))÷(sqrt(1-x^2-y^2))= 7/4 .

(sqrt(1-x^2-y^2) is common in both.

Reply 3

alevelmath1

After simplification I got above .

Reply 4

mqb2766

Original post by alevelmath1

After simplification I got above .

Do you have the original question (link / picture)? Where does it come from?

You can do some basic reasoning to justify that both x and y are positive, less than 1 and y<x. In additon, they must be roughly equal and so 0.6 to 0.7 in value. However, cant see an elegant way to get a closed form solution using those equations.