If a + b + c = 11, ab + bc + ca = 3 and abc = —135, then what is the value of a3 + b3 + c3 ?
Answer & explanation
Correct answer: option 2
a + b + c = 11,
ab + bc + ca = 3
abc = -135
a3 + b3 + c3 – 3abc = (a + b + c) [(a + b + c)2 – 3(ab + bc + ca)]
= a3 + b3 + c3 – 3 × (-135) = 11 [112 – 3 × 3]
= a3 + b3 + c3 + 405 = 11 × [121 – 9]
= a3 + b3 + c3 = 1232 – 405
= a3 + b3 + c3 = 827