x + y = 3, x2+ y2= 5 হলে, x3+ y3= ?

প্রশ্ন: x + y = 3, x² + y² = 5 হলে, x³ + y³ = ?

সমাধান:
x + y = 3
x² + y² = 5

এখন
(x + y)² = x² + y² + 2xy
⇒ 3² = 5 + 2xy
⇒ 9 - 5 = 2xy
⇒ 2xy = 4
∴ xy = 2

x³ + y³ = (x + y)³ - 3xy(x + y)
⇒ x³ + y³ = 3³ - 3 × 2 × 3
⇒ x³ + y³ = 27 - 18
∴ x³ + y³ = 9