let-a-b-c-x-y-and-z-be-complex-numbers-such-that-a-b-c-x-2-b-c-a-y-2-c-a-b-z-2-if-xy-yz-zx-1000-and-x-y-z-2016-find-the-value-of-xyz-

Tinku Tara June 4, 2023 None 0 Comments

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=((b+c)/(x−2)), b=((c+a)/(y−2)), c=((a+b)/(z−2)) if xy+yz+zx=1000 and x+y+z=2016, find the value of xyz

$${let}\:{a},{b},{c},{x},{y}\:{and}\:{z}\:{be}\:{complex}\:{numbers} \\ $$$${such}\:{that}\:: \\ $$$${a}=\frac{{b}+{c}}{{x}−\mathrm{2}},\:{b}=\frac{{c}+{a}}{{y}−\mathrm{2}},\:{c}=\frac{{a}+{b}}{{z}−\mathrm{2}} \\ $$$${if}\:{xy}+{yz}+{zx}=\mathrm{1000}\:{and}\:{x}+{y}+{z}=\mathrm{2016}, \\ $$$${find}\:{the}\:{value}\:{of}\:{xyz} \\ $$

Commented by ajfour last updated on 13/Mar/23

$${anyone}? \\ $$

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let-a-b-c-x-y-and-z-be-complex-numbers-such-that-a-b-c-x-2-b-c-a-y-2-c-a-b-z-2-if-xy-yz-zx-1000-and-x-y-z-2016-find-the-value-of-xyz-

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