that simultaneously satisfy the conditions 
and![\[
\frac{x^4}{a} - \frac{y^4}{b} = \frac{1}{a - b}.
\]](http://latex.artofproblemsolving.com/4/5/e/45e29c956890cb0bd869c67e7ad94c92d868d2e2.png)
,![\[
\left( \frac{x^2}{a} \right)^n + \left( \frac{y^2}{b} \right)^n = \frac{2}{(a - b)^n}.
\]](http://latex.artofproblemsolving.com/4/0/5/405491f7aae19de4c7ad1f90da3d66e4038e3299.png)
and 
.
Equality holds when 
or 
or 
for all 
.
and 
, then we can deduce 
\le 2 $ ?
Y by Adventure10
The vertices of a right-angled triangle are on a circle of radius 
and the sides of the triangle are tangent to another circle of radius 
(this is the circle that is inside triangle). If the lengths of the sides about the right angles are 16 and 30, determine the value of 
.
and the sides of the triangle are tangent to another circle of radius 
(this is the circle that is inside triangle). If the lengths of the sides about the right angles are 16 and 30, determine the value of 
.
