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SSC Selection Post 2019 PYQ — Question 58

SSC Selection Post - Matriculation Level 2019 - 14 Oct 2019 - Shift 1 • Quantitative Aptitude • Q58

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If a + b + c = 7, and a² + b²+c² = 33, then what is the value of a3 + b3 + c3 - 3abc? 

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 175.

a+b+c=7,a2+b2+c2=33(a+b+c)2=49=33+2(ab+bc+ca)⇒ab+bc+ca=49−332=8a + b + c = 7,\quad a^2 + b^2 + c^2 = 33 \\ (a + b + c)^2 = 49 = 33 + 2(ab + bc + ca) \\ \Rightarrow ab + bc + ca = \frac{49 - 33}{2} = 8

a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)=7(33−8)=7×25=175a^3 + b^3 + c^3 - 3abc = (a + b + c)\left(a^2 + b^2 + c^2 - ab - bc - ca\right) \\ = 7(33 - 8) = 7 \times 25 = 175