Correct Answer - Option 1 : 815
Given:
a + b + c = 14, ab + bc + ca = 47 and abc = 15
Concept used:
a³ + b³ + c³ - 3abc = a + b + c × [(a + b + c)² -3(ab + bc + ca)]
Calculations:
a³ + b³ + c³ - 3abc = 14 × [(14)² - 3 × 47]
⇒ a³ + b³ + c³ – 3 × 15 = 14(196 – 141)
⇒ a³ + b³ + c³ = 14(55) + 45
⇒ 770 + 45
⇒ 815
∴ The correct choice is option 1.
