If x + y = 12 and x − y = 4, find: (x³ + y³) / (x + y)
Show answer & explanation
Correct answer: A
Explanation
Given:
x + y = 12
x − y = 4
By the formula:
x³ + y³ = (x + y)³ − 3xy(x + y)
(x + y)² = (x − y)² + 4xy
12² = 4² + 4xy
14³ = 16 + 4xy
4xy = 128
xy = 32
x³ + y³ = (12)³ − 3 × 32 × 12
= 1728 − 1152
= 576
(x³ + y³) / (x + y) = 576 / 12 = 48