if (a+b+c)+(ab+bc+ca)+(a*b*c)=100, then find a+b+c

Kindly cross check, the correct statement of the given condition should be (a+b+c)+(ab+bc+ca)+(a*b*c)=1000

 

Answer:

 

Consider the product (a+1)(b+1)(c+1).

 

(a+1)(b+1)(c+1) = a+d+c+ab+bc+ca+abc+1 

So we can rewrite the goven equation as
(a+1)(b+1)(c+1) - 1 = 1000 
(a+1)(b+1)(c+1) = 1001 
(a+1)(b+1)(c+1) = 7*11*13 
(a+1)(b+1)(c+1) = (6+1)*(10+1)*(12+1) 

Thus, a+b+c = 6+10+12=28