If x4 + x2y2 + y4 = 24 x2 + y2 + xy = 6 x3 - y3 = ?

x⁴ + x²y² + y⁴ = 24

x² + y² + xy = 6

x⁴ + x²y² + y⁴ = 24

2(x² + y²) = 10

x² + y² = 5

Put in x² + y² + xy = 6

5 + xy = 6

xy = 1

If x² + y² = 5

then x - y = \(\sqrt {5-2}\) 

x - y = \(\sqrt {3}\) 

x³ - y³ = (x-y)(x² + y² + xy)

\(\sqrt {3}\) × 6

6\(\sqrt {3}\)