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SSC Selection Post 2022 PYQ — Question 65

SSC Selection Post - Higher Secondary Level 2022 - 15 March 2022 - Shift 2 • Quantitative Aptitude • Q65

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If x + y + z = 4, xy + yz + zx = 1 and x3 + y3 + z3 = 34, then what is the value of 6xyz?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. -36.

x3+y3+z3=(x+y+z)3−3(x+y+z)(xy+yz+zx)+3xyz\\ x^3 + y^3 + z^3 = (x + y + z)^3 - 3(x + y + z)(xy + yz + zx) + 3xyz

\begin{align*} 34 &= 4^3 - 3(4)(1) + 3xyz \\ 34 &= 64 - 12 + 3xyz \\ 34 &= 52 + 3xyz \\ 3xyz &= 34 - 52 = -18 \\ 6xyz &= 2 \cdot (-18) = \boxed{-36} \end{align*}