If a + b + c = 15, ab + bc + ca = 48 and abc = 16, then find the value of a³ + b³ + c³.
Show answer & explanation
Correct answer: B
Explanation
a + b + c = 15, ab + bc + ca = 48, abc = 16
According to the formula:
a³ + b³ + c³ = (a + b + c)³ − 3(a + b + c)(ab + bc + ca) + 3abc
= 15³ − 3 × 15 × 48 + 3 × 16
= 3375 − 2160 + 48
= 1263