Question

If,
abc+(ab+bc+ac)+a+b+c=1000
Then,
Find a+b+c in numerical value.

Answer 1

We know that

a + b + c + ab + bc + ac + abc + 1 = (a + 1) (b + 1) (c + 1)

Given : a + b + c + ab + bc + ac + abc = 1000

⇒ (a + 1) (b + 1) (c + 1) – 1 = 1000

⇒ (a + 1) (b + 1) (c + 1) = 1001

Now the prime factors of 1001 are 7, 11 and 13

So,

(a + 1) (b + 1) (c + 1) = 7 × 11 × 13

⇒ (a + 1) (b + 1) (c + 1) = (6 + 1) (10 + 1) (12 + 1)

Thus the values of a, b, c are 6, 10, 12
So a+b+c = 28