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SSC CHSL 2019 PYQ — Question 55

SSC CHSL - 2nd July 2019 - Shift 2 • Quantitative Aptitude • Q55

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If a + b + c = 4 and ab + bc + ca = 1, then the value of a3 + b3 + c3 – 3abc is:

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Correct answer: A

Explanation

Correct Answer is option 1 i.e. 52

Application

Given:

a + b + c = 4 and ab + bc + ca = 1

a + b + c = 4

Taking square:

a2 + b2 + c2 + 2(ab + bc + ca) = 16

a2 + b2 + c2 = 16 – 2 = 14

Now,

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

= 4 (14 – 1) = 52