Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a3 + b3 + c3 ?
Option 1: 67
Option 2: –53
Option 3: –51
Option 4: 27
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Correct Answer: –53
Solution :
Given: $a + b + c = 1$
$ab + bc + ca = -22$
$abc = -40$
Using the below equation:
$a^3+b^3+c^3−3abc=(a+b+c)[(a+b+c)^2−3(ab+bc+ca)]$
$⇒a^3+b^3+c^3−3abc = (1)[(1)^2 - 3(-22)]$
$⇒a^3+b^3+c^3−3abc = 67$
$⇒a^3+b^3+c^3 = 3abc + 67$
$⇒a^3+b^3+c^3 = 3(-40) + 67$
$⇒a^3+b^3+c^3 = -53$
Hence, the correct answer is –53.
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