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?
Divya Ranjan Pattanaik , 8 Years ago
Grade 8
8 grade maths> If abc+ab+bc+ca+a+b+c = 1000 then find th...
1 AnswersNishant Vora
Last Activity: 8 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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