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SSC Selection Post 2022 PYQ — Question 73

SSC Selection Post - Matriculation Level 2022 - 7 Feb 2022 - Shift 1 • Quantitative Aptitude • Q73

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If a + b + c = 1, ab + bc + ca = -8 and a3 + b3 +  c3  = -11, then what is the value of abca\over{bc} + bacb\over{ac} + cabc\over{ab}?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. −1712-17\over12.

a2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca)

⇒ a2 + b2 + c2 = 1 - 2(-8)

⇒ a2 + b2 + c2 = 17

a3 + b3 +  c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

⇒ -11 - 3abc = 17 + 8

⇒ abc = -12

Now, Dividing (a2 + b2 + c2) by abc,

⇒ abca\over{bc} + bacb\over{ac} + cabc\over{ab} = −1712-17\over12