Interesting Maths Q3 (Hard)

Let x⁴= a and y⁴= b , then
(x⁴/ y⁴+ y⁴/ x⁴)/4 + 4(xy)⁴/ [x⁸ + 2(xy)⁴+ y⁸] - 3/2
= (a/b + b/a)/4 + 4ab / [a² + 2ab + b²] - 3/2
= (a² + b²) / (4ab) + 4ab / (a + b)² - 3/2
= ( (a + b)² - 2ab ) / (4ab) + 4ab / (a + b)² - 3/2
= (a + b)² / (4ab) + 4ab / (a + b)² - 2
= ( (a + b)⁴+ 16a²b² - 8ab (a + b)² ) / ( 4ab (a + b)² )
= ( (a + b)² - 4ab )² / ( 4ab (a + b)² )
= (a - b)⁴/ ( 4ab (a + b)² )
= [ (a - b)² / (2 √a √b (a + b)) ] ²
= [ ( x⁴- y⁴)² / ( 2 x² y² ( x⁴+ y⁴) ) ] ²
= [ (x - y)² (x + y)² (x² + y²)² / ( 2 x² y² ( x⁴+ y⁴) ) ] ²

2011-11-05 02:13:37 補充：
OH! You are the designer of this question , thank you very much !