[JEE Advanced 1990] if x 0 y 0 with x y xy 12 and x y xy
If $x<0,y<0$ with $x+y+\frac xy=\frac12$ and $(x+y)\frac xy=-\frac12$, then $x=$ ____ and $y=$ ____
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Answer: $x=-\frac14,\ y=-\frac14$.
$u=x+y,v=\frac xy$ satisfy $u+v=\frac12,uv=-\frac12$, so $\{u,v\}=\{1,-\frac12\}$. As $\frac xy>0$, $v=1\Rightarrow x=y$ and $u=-\frac12\Rightarrow x=y=-\frac14$.
JEE Advanced 1990 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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