If x3 + y3 = 152 x + y = 8 Find the value of x4 + y4 + 14.

x³ + y³ = 152

x + y = 8

(x + y)³ = x³ + y³ + 3xy (x + y)

512 = 152 + 24xy

xy = \(\frac{360}{24}\)

xy = 15

⇒ x² + y² = 64 - 2 × 15

⇒ x² + y² = 34

⇒ x⁴ + y⁴ = (34)² - 2 × 15 × 15

⇒ x⁴ + y⁴ = 1156 - 450 = 706

x⁴ + y⁴ + 14 = 706 + 14

= 720