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Xyz+xy+yz+zx+x+y+z =384 find x+y+zFind answer................?..................?....................? .. ....... ............ ......

Xyz+xy+yz+zx+x+y+z =384 find x+y+zFind answer................?..................?....................? .. ....... ............ ......

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Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Sneha
 
Xyz+xy+xz+yz+x+y+z=384
xy (z+1) + z (x+y)+1(x+y)+z=384
xy (z+1) + (x+y) (z+1) +(z+1)−1=384
xy (z+1) + (x+y) (z+1) +(z+1)=385
(z+1) (xy+x+y+1)=385
(z+1) (x(y+1)+1(y+1))=385
(x+1)(y+1)(z+1)=385
(x+1)(y+1)(z+1)=5×7×11
On comparing ,x+1 = 5 , y+1=7 , z+1=11or x+1 = 7 , y+1=11 , z+1=5or x+1 = 11 , y+1=5 , z+1=7Now , 
For each case
x+1+y+1+z+1=5+11+7x+y+z+3=23
x+y+z=20   ANS
 
 
Regards
Arun (askIITians forum expert)

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