Quadratic equation system with three variables
Source: 0
April 23, 2009
quadratics
Problem Statement
If x^{2} \plus{}y^{2} \plus{}z\equal{}15, x\plus{}y\plus{}z^{2} \equal{}27 and xy\plus{}yz\plus{}zx\equal{}7, then(A)\ 3\le \left|x\plus{}y\plus{}z\right|\le 4 \\ (B)\ 5\le \left|x\plus{}y\plus{}z\right|\le 6 \\ (C)\ 7\le \left|x\plus{}y\plus{}z\right|\le 8 \\ (D)\ 9\le \left|x\plus{}y\plus{}z\right|\le 10 \\ (E)\ \text{None}