Question
Download Solution PDFIf a + b + c = 14, ab + bc + ca = 47 and abc = 15 then find the value of a3 + b3 +c3.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
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