Question Number 17782 by Mr easymsn last updated on 10/Jul/17
$${let}\:{a},{b},{c},{x},{y}\:{and}\:{z}\:{be}\:{complex}\:{numbers} \\ $$$${such}\:{that}\:: \\ $$$${a}=\frac{{b}+{c}}{{x}−\mathrm{2}},\:{b}=\frac{{c}+{a}}{{y}−\mathrm{2}},\:{c}=\frac{{a}+{b}}{{z}−\mathrm{2}} \\ $$$${if}\:{xy}+{yz}+{zx}=\mathrm{1000}\:{and}\:{x}+{y}+{z}=\mathrm{2016}, \\ $$$${find}\:{the}\:{value}\:{of}\:{xyz} \\ $$
Commented by ajfour last updated on 13/Mar/23
$${anyone}? \\ $$