N-is-a-number-N-which-has-three-digits-and-written-xyz-in-base-10-such-that-xy-xz-yz-xyz-0-lt-x-lt-y-lt-z-Determinate-N-

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

N i s a n u m b e r \in N w h i c h h a s t h r e e

d i g i t s a n d w r i t t e n x y z i n b a s e 10

s u c h t h a t {\begin{cases} x y + x z + y z = x y z \\ 0 < x < y < z \end{cases}

D e t e r m i n a t e N .

Commented by JDamian last updated on 24/Dec/20

P l e a s e, w h a t d o e s \boldsymbol x y s t a n d f o r ?

a) p r o d u c t o f \boldsymbol x a n d \boldsymbol y - - x \times y

b) t w o d i g i t n u m b e r w h e r e \boldsymbol x a n d \boldsymbol y a r e t w o

d i g i t s o f t h e n u m b e r N w e a r e l o o k i n g f o r .

Commented by mathocean1 last updated on 24/Dec/20

I {d o n}^{'} t t h i n k s o s i r \dots i f o u n d t h i s

e x e r c i s e i n s o m e b o o k . B u t i n m y

o p i n i o n x y s t a n d f o r t h e t h e o p t i o n

b y o u d e s c r i b e d \dots y o u c a n d o i t a s i t

s e e m s n o r m a l f o r y o u s i r \dots

Commented by mathocean1 last updated on 24/Dec/20

s o i t m a y b e o p t i o n a

s o i t m a y b e o p t i o n a