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Question Number 126795 by mathocean1 last updated on 24/Dec/20

N is a number ∈ N which has three  digits and written xyz in base 10   such that  { ((xy+xz+yz=xyz)),((0<x<y<z)) :}  Determinate N.

$${N}\:{is}\:{a}\:{number}\:\in\:\mathbb{N}\:{which}\:{has}\:{three} \\ $$ $${digits}\:{and}\:{written}\:{xyz}\:{in}\:{base}\:\mathrm{10}\: \\ $$ $${such}\:{that}\:\begin{cases}{{xy}+{xz}+{yz}={xyz}}\\{\mathrm{0}<{x}<{y}<{z}}\end{cases} \\ $$ $${Determinate}\:{N}. \\ $$

Commented byJDamian last updated on 24/Dec/20

Please, what does  xy stand for?  a) product of x and y −− x × y  b) two digit number where x and y are two  digits of the number N we are looking for.

$${Please},\:{what}\:{does}\:\:\boldsymbol{{xy}}\:{stand}\:{for}? \\ $$ $$\left.{a}\right)\:{product}\:{of}\:\boldsymbol{{x}}\:{and}\:\boldsymbol{{y}}\:−−\:{x}\:×\:{y} \\ $$ $$\left.{b}\right)\:{two}\:{digit}\:{number}\:{where}\:\boldsymbol{{x}}\:{and}\:\boldsymbol{{y}}\:{are}\:{two} \\ $$ $${digits}\:{of}\:{the}\:{number}\:{N}\:{we}\:{are}\:{looking}\:{for}. \\ $$

Commented bymathocean1 last updated on 24/Dec/20

I don′t think so sir...i found this   exercise in some book. But in my  opinion xy stand for the  the option  b you described... you can do it as it  seems normal for you sir...

$${I}\:{don}'{t}\:{think}\:{so}\:{sir}...{i}\:{found}\:{this}\: \\ $$ $${exercise}\:{in}\:{some}\:{book}.\:{But}\:{in}\:{my} \\ $$ $${opinion}\:{xy}\:{stand}\:{for}\:{the}\:\:{the}\:{option} \\ $$ $${b}\:{you}\:{described}...\:{you}\:{can}\:{do}\:{it}\:{as}\:{it} \\ $$ $${seems}\:{normal}\:{for}\:{you}\:{sir}... \\ $$

Commented bymathocean1 last updated on 24/Dec/20

so it may be option a

$${so}\:{it}\:{may}\:{be}\:{option}\:{a} \\ $$

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