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If abc+ab+bc+ca+a+b+c = 1000 then find the value of a+b+c?

If abc+ab+bc+ca+a+b+c = 1000 then find the value of a+b+c?

Grade:8

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Dear student,

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

So we can rewrite this equation
a+b+c+ab+bc+ca+abc=1000

as

(a+1)(b+1)(c+1) - 1 = 1000
so
(a+1)(b+1)(c+1) = 1001

which can be re written as
(a+1)(b+1)(c+1) = 7*11*13

if you look at this eqn closesly, these 7, 11 and 13 are prime numbers and can be rewritten as (6+1)*(10+1)*(12+1)

So you can find that a+b+c = 28.

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