if a, b, c are three positive numbers then abc +ab+bc+ac+a+b+c=1000,then a+b+c=?
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Question :- If abc+ab+bc+ca+a+b+c = 1000 then find the value of a+b+c?
Answer = (a+1)(b+1)(c+1) = a+d+c+ab+bc+ca+abc+1
we can write this equation as a+b+c+ab+bc+ca+abc=1000
(a+1)(b+1)(c+1)-1=1000
(a+1)(b+1)(c+1) = 1001
so it can be written as (a+1)(b+1)(c+1) = 7*11*13
7, 11 and 13 are prime numbers and can be rewritten as (6+1)*(10+1)*(12+1)
You can see that a+b+c = 28.
Question :- If abc+ab+bc+ca+a+b+c = 1000 then find the value of a+b+c?
Answer = (a+1)(b+1)(c+1) = a+d+c+ab+bc+ca+abc+1
we can write this equation as a+b+c+ab+bc+ca+abc=1000
(a+1)(b+1)(c+1)-1=1000
(a+1)(b+1)(c+1) = 1001
so it can be written as (a+1)(b+1)(c+1) = 7*11*13
7, 11 and 13 are prime numbers and can be rewritten as (6+1)*(10+1)*(12+1)
You can see that a+b+c = 28.
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