InterviewSolution
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InterviewSolution
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If \(x + y + z = 3\) and \(xy + yz + zx=-11\), then what is the value of \({x^3} + {y^3} + {z^3} - 3xyz\)?1. 1262. 1453. 1214. 154 |
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Answer» Correct Answer - Option 1 : 126 Given: x + y + z = 3 and xy + yz + zx = -11 Concept used: Algebra Calculation: (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx) Using the above values in the equation, ⇒ (3)2 = x2 + y2 + z2 + 2(-11) ⇒ x2 + y2 + z2 = 22 + 9 ⇒ x2 + y2 + z2 = 31 \({x^3} + {y^3} + {z^3} - 3xyz\) = (x + y + z) [(x2 + y2 + z2 - (xy + yz + zx)] \({x^3} + {y^3} + {z^3} - 3xyz\) = (3) [(31 + 11)] \({x^3} + {y^3} + {z^3} - 3xyz\) = 126 |
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