If a + b + c = 1, ab + bc + ca = -22 and abc = -40, then what is the value of a3 + b3 + c3 ?
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Correct answer: A
Explanation
The correct answer is option 1 i.e. -53.
⇒ a + b + c = 1
on squaring both sides we get,
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 1
⇒ a2 + b2 + c2 = 1 + 44 = 45.
⇒ a3 + b3 + c3 - 3abc = (a + b + c)( a2 + b2 + c2 - ab - bc - ca)
⇒ a3 + b3 + c3 = 1 × (45 + 22) - 3 × 40
⇒ a3 + b3 + c3 = 67 - 120 = -53