Question

If x + y = 8 and x2 + y2 = 40, find the value of x3 + y3.

Answer 1

Given,
x + y = 8
x² + y² = 40
so,
(x + y)² = (x² + y²) + 2xy
8² = 40 + 2xy
24 = 2xy
12 = xy
now,
x³ + y³ = (x + y)³ -3xy(x + y)
= (8)³ - 3×12 × 8
= 512 - 288
= 224

Answer 2

x+y = 8
x²+y² = 40

⭐x³ + y³ = (x+y)³ - 3xy(x + y)⭐

we need to find, value of xy

(x+y)² = x²+y² + 2xy

8² = 40 + 2xy

64 - 40 = 2xy

xy = 24/2

xy = 12

x³ + y³ = (8)³ - 3(12)(8)

= 512 - 288

= 224

hope it helps